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Journal articles on the topic 'Abelianization'

Author: Grafiati

Published: 25 May 2024

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1

SATO, MASATOSHI. "The abelianization of a symmetric mapping class group." Mathematical Proceedings of the Cambridge Philosophical Society 147, no. 2 (September 2009): 369–88. http://dx.doi.org/10.1017/s0305004109002576.

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AbstractLet Σg,r be a compact oriented surface of genus g with r boundary components. We determine the abelianization of the symmetric mapping class group (g,r)(p2) of a double unbranched cover p2: Σ2g − 1,2r → Σg,r using the Riemann constant, Schottky theta constant, and the theta multiplier. We also give lower bounds on the order of the abelianizations of the level d mapping class group.

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2

SATOH, TAKAO. "The abelianization of the congruence IA-automorphism group of a free group." Mathematical Proceedings of the Cambridge Philosophical Society 142, no. 2 (March 2007): 239–48. http://dx.doi.org/10.1017/s0305004106009959.

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AbstractWe consider the abelianizations of some normal subgroups of the automorphism group of a finitely generated free group. Let Fn be a free group of rank n. For d ≥ 2, we consider a group consisting the automorphisms of Fn which act trivially on the first homology group of Fn with ${\mathbf Z}$/d${\mathbf Z}$-coefficients. We call it the congruence IA-automorphism group of level d and denote it by IAn,d. Let IOn,d be the quotient group of the congruence IA-automorphism group of level d by the inner automorphism group of a free group. We determine the abelianization of IAn,d and IOn,d for n ≥ 2 and d ≥ 2. Furthermore, for n=2 and odd prime p, we compute the integral homology groups of IA2,p for any dimension.

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3

Ratcliffe, John G., and Steven T. Tschantz. "Abelianization of space groups." Acta Crystallographica Section A Foundations of Crystallography 65, no. 1 (November 18, 2008): 18–27. http://dx.doi.org/10.1107/s0108767308036222.

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4

Hausel, Tamás, and Nicholas Proudfoot. "Abelianization for hyperkähler quotients." Topology 44, no. 1 (January 2005): 231–48. http://dx.doi.org/10.1016/j.top.2004.04.002.

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5

Blachar, Guy, Orit Sela–Ben-David, and Uzi Vishne. "Abelianization of the Cartwright-Steger lattice." Algebra and Discrete Mathematics 34, no. 2 (2022): 176–86. http://dx.doi.org/10.12958/adm1966.

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The Cartwright-Steger lattice is a group whose Cayley graph can be identified with the Bruhat-Tits building of PGLd over a local field of positive characteristic. We give a lower bound on the abelianization of this lattice, and report that the bound is tight in all computationally accessible cases.

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6

Wehrfritz, B. A. F. "The abelianization of hypercyclic groups." Central European Journal of Mathematics 5, no. 4 (December 2007): 686–95. http://dx.doi.org/10.2478/s11533-007-0030-4.

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7

Loran, F. "Abelianization of first class constraints." Physics Letters B 547, no. 1-2 (October 2002): 63–68. http://dx.doi.org/10.1016/s0370-2693(02)02734-x.

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8

Kamgarpour, Masoud. "Stacky abelianization of algebraic groups." Transformation Groups 14, no. 4 (October 31, 2009): 825–46. http://dx.doi.org/10.1007/s00031-009-9067-8.

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9

Nunes, João P., and Howard J. Schnitzer. "Field Strength Correlators for Two-Dimensional Yang–Mills Theories Over Riemann Surfaces." International Journal of Modern Physics A 12, no. 26 (October 20, 1997): 4743–68. http://dx.doi.org/10.1142/s0217751x9700253x.

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The path integral computation of field strength correlation functions for two-dimensional Yang–Mills theories over Riemann surfaces is studied. The calculation is carried out by Abelianization, which leads to correlators that are topological. They are nontrivial as a result of the topological obstructions to the Abelianization. It is shown in the large N limit on the sphere that the correlators undergo second order phase transitions at the critical point. Our results are applied to a computation of contractible Wilson loops.

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10

Dimca, Alexandru, Richard Hain, and Stefan Papadima. "The abelianization of the Johnson kernel." Journal of the European Mathematical Society 16, no. 4 (2014): 805–22. http://dx.doi.org/10.4171/jems/447.

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11

Bourn, Dominique, and Zurab Janelidze. "A Note on the Abelianization Functor." Communications in Algebra 44, no. 5 (April 25, 2016): 2009–33. http://dx.doi.org/10.1080/00927872.2014.982808.

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12

Holm, Tara S., and Reyer Sjamaar. "Torsion and Abelianization in Equivariant Cohomology." Transformation Groups 13, no. 3-4 (September 10, 2008): 585–615. http://dx.doi.org/10.1007/s00031-008-9023-z.

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13

Bitton, Charly. "The abelianization of almost free groups." Proceedings of the American Mathematical Society 129, no. 6 (November 21, 2000): 1799–803. http://dx.doi.org/10.1090/s0002-9939-00-05730-0.

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14

Gogilidze, S. A., A. M. Khvedelidze, and V. N. Pervushin. "On Abelianization of first class constraints." Journal of Mathematical Physics 37, no. 4 (April 1996): 1760–71. http://dx.doi.org/10.1063/1.531478.

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15

Oancea, D. "Coessential Abelianization Morphisms in the Category of Groups." Canadian Mathematical Bulletin 56, no. 2 (June 1, 2013): 395–99. http://dx.doi.org/10.4153/cmb-2011-172-3.

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Abstract.An epimorphism ϕ: G → H of groups, where G has rank n, is called coessential if every (ordered) generating n-tuple of H can be lifted along ϕ to a generating n-tuple for G. We discuss this property in the context of the category of groups, and establish a criterion for such a group G to have the property that its abelianization epimorphism G → G/[G, G], where [G,G] is the commutator subgroup, is coessential. We give an example of a family of 2-generator groups whose abelianization epimorphism is not coessential. This family also provides counterexamples to the generalized Andrews–Curtis conjecture.

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16

Cha, Jae Choon, Stefan Friedl, and Taehee Kim. "The cobordism group of homology cylinders." Compositio Mathematica 147, no. 3 (September 7, 2010): 914–42. http://dx.doi.org/10.1112/s0010437x10004975.

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AbstractGaroufalidis and Levine introduced the homology cobordism group of homology cylinders over a surface. This group can be regarded as an enlargement of the mapping class group. Using torsion invariants, we show that the abelianization of this group is infinitely generated provided that the first Betti number of the surface is positive. In particular, this shows that the group is not perfect. This answers questions of Garoufalidis and Levine, and Goda and Sakasai. Furthermore, we show that the abelianization of the group has infinite rank for the case that the surface has more than one boundary component. These results also hold for the homology cylinder analogue of the Torelli group.

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17

Bazzoni, Silvana, and Jan Šťovíček. "On the abelianization of derived categories and a negative solution to Rosický’s problem." Compositio Mathematica 149, no. 1 (November 6, 2012): 125–47. http://dx.doi.org/10.1112/s0010437x12000413.

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AbstractWe prove for a large family of rings R that their λ-pure global dimension is greater than one for each infinite regular cardinal λ. This answers in the negative a problem posed by Rosický. The derived categories of such rings then do not satisfy, for any λ, the Adams λ-representability for morphisms. Equivalently, they are examples of well-generated triangulated categories whose λ-abelianization in the sense of Neeman is not a full functor for any λ. In particular, we show that given a compactly generated triangulated category, one may not be able to find a Rosický functor among the λ-abelianization functors.

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18

SATOH, TAKAO. "The kernel of the Magnus representation of the automorphism group of a free group is not finitely generated." Mathematical Proceedings of the Cambridge Philosophical Society 151, no. 3 (July 18, 2011): 407–19. http://dx.doi.org/10.1017/s0305004111000338.

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19

HIROSE, SUSUMU, and MASATOSHI SATO. "A minimal generating set of the level 2 mapping class group of a non-orientable surface." Mathematical Proceedings of the Cambridge Philosophical Society 157, no. 2 (July 30, 2014): 345–55. http://dx.doi.org/10.1017/s0305004114000358.

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20

Kocherova, A., and I. Zhdanovskiy. "Partial Abelianization of Free Product of Algebras." Lobachevskii Journal of Mathematics 42, no. 10 (October 2021): 2348–57. http://dx.doi.org/10.1134/s1995080221100115.

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21

Borovoi, Mikhail V. "Abelianization of the second nonabelian Galois cohomology." Duke Mathematical Journal 72, no. 1 (October 1993): 217–39. http://dx.doi.org/10.1215/s0012-7094-93-07209-2.

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22

Gisin, V. B. "Abelianization and orthogonal complements of additive categories." Communications in Algebra 24, no. 6 (January 1996): 2025–63. http://dx.doi.org/10.1080/00927879608825687.

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23

Abe, Ryuji. "Abelianization of Fricke groups and rhombic lattices." Indagationes Mathematicae 11, no. 3 (September 2000): 317–35. http://dx.doi.org/10.1016/s0019-3577(00)80001-4.

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24

dos Santos, Pedro F., and Zhaohu Nie. "Stable equivariant abelianization, its properties, and applications." Topology and its Applications 156, no. 5 (February 2009): 979–96. http://dx.doi.org/10.1016/j.topol.2008.11.015.

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25

Barnea, Ilan, and Saharon Shelah. "The abelianization of inverse limits of groups." Israel Journal of Mathematics 227, no. 1 (July 21, 2018): 455–83. http://dx.doi.org/10.1007/s11856-018-1741-x.

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26

Gnanapragasam, B., and H. S. Sharatchandra. "Abelianization of non-Abelian lattice gauge theories." Physical Review D 45, no. 4 (February 15, 1992): R1010—R1012. http://dx.doi.org/10.1103/physrevd.45.r1010.

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27

Zimmermann, Susanna. "The Abelianization of the real Cremona group." Duke Mathematical Journal 167, no. 2 (February 2018): 211–67. http://dx.doi.org/10.1215/00127094-2017-0028.

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28

SATOH, TAKAO. "The abelianization of the congruence IA-automorphism group of a free group." Mathematical Proceedings of the Cambridge Philosophical Society 143, no. 1 (July 2007): 255–56. http://dx.doi.org/10.1017/s0305004107000382.

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29

Yoshida, Tomoyoshi. "An abelianization of the SU(2) WZW model." Annals of Mathematics 164, no. 1 (July 1, 2006): 1–49. http://dx.doi.org/10.4007/annals.2006.164.1.

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30

Hollands, Lotte, and Andrew Neitzke. "Exact WKB and Abelianization for the $$T_3$$ Equation." Communications in Mathematical Physics 380, no. 1 (October 13, 2020): 131–86. http://dx.doi.org/10.1007/s00220-020-03875-1.

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31

BISWAS, INDRANIL, and JOÃO PEDRO P. DOS SANTOS. "Abelianization of the F-divided fundamental group scheme." Proceedings - Mathematical Sciences 127, no. 2 (December 2, 2016): 281–87. http://dx.doi.org/10.1007/s12044-016-0322-3.

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32

Hwang, Stephen. "Abelianization of gauge algebras in the Hamiltonian formalism." Nuclear Physics B 351, no. 1-2 (March 1991): 425–40. http://dx.doi.org/10.1016/0550-3213(91)90096-g.

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33

Marnelius, Robert. "Gauge fixing and abelianization in simple BRST quantization." Nuclear Physics B 412, no. 3 (January 1994): 817–33. http://dx.doi.org/10.1016/0550-3213(94)90399-9.

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34

Corson, Samuel M. "Freely indecomposable almost free groups with free abelianization." Journal of Group Theory 23, no. 3 (May 1, 2020): 531–43. http://dx.doi.org/10.1515/jgth-2019-0102.

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AbstractFor certain uncountable cardinals κ, we produce a group of cardinality κ which is freely indecomposable, strongly κ-free, and whose abelianization is free abelian of rank κ. The construction takes place in Gödel’s constructible universe L. This strengthens an earlier result of Eklof and Mekler.

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35

Sato, Masatoshi. "The abelianization of the level d mapping class group." Journal of Topology 3, no. 4 (2010): 847–82. http://dx.doi.org/10.1112/jtopol/jtq026.

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36

Webb, Rachel. "Abelianization and quantum Lefschetz for orbifold quasimap I-functions." Advances in Mathematics 439 (March 2024): 109489. http://dx.doi.org/10.1016/j.aim.2024.109489.

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37

SILVER, DANIEL S., and SUSAN G. WILLIAMS. "ALEXANDER GROUPS AND VIRTUAL LINKS." Journal of Knot Theory and Its Ramifications 10, no. 01 (February 2001): 151–60. http://dx.doi.org/10.1142/s0218216501000792.

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The extended Alexander group of an oriented virtual link l of d components is defined. From its abelianization a sequence of polynomial invariants Δi (u1,…,ud, v), i=0, 1,…, is obtained. When l is a classical link, Δi reduces to the well-known ith Alexander polynomial of the link in the d variables u1v,…,udv; in particular, Δ0 vanishes.

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38

Fel’shtyn, Alexander, Jang Hyun Jo, and Jong Bum Lee. "Growth rate for endomorphisms of finitely generated nilpotent groups." Journal of Group Theory 23, no. 6 (November 1, 2020): 945–64. http://dx.doi.org/10.1515/jgth-2020-0097.

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AbstractWe prove that the growth rate of an endomorphism of a finitely generated nilpotent group is equal to the growth rate of the induced endomorphism on its abelianization, generalizing the corresponding result for an automorphism in [T. Koberda, Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups, In the Tradition of Ahlfors–Bers. VI, Contemp. Math. 590, American Mathematical Society, Providence 2013, 87–99].

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39

Bächle, Andreas, Sugandha Maheshwary, and Leo Margolis. "Abelianization of the unit group of an integral group ring." Pacific Journal of Mathematics 312, no. 2 (August 31, 2021): 309–34. http://dx.doi.org/10.2140/pjm.2021.312.309.

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40

Rahm, Alexander D. "Higher torsion in the Abelianization of the full Bianchi groups." LMS Journal of Computation and Mathematics 16 (2013): 344–65. http://dx.doi.org/10.1112/s1461157013000168.

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AbstractDenote by $ \mathbb{Q} ( \sqrt{- m} )$, with $m$ a square-free positive integer, an imaginary quadratic number field, and by ${ \mathcal{O} }_{- m} $ its ring of integers. The Bianchi groups are the groups ${\mathrm{SL} }_{2} ({ \mathcal{O} }_{- m} )$. In the literature, so far there have been no examples of $p$-torsion in the integral homology of the full Bianchi groups, for $p$ a prime greater than the order of elements of finite order in the Bianchi group, which is at most 6. However, extending the scope of the computations, we can observe examples of torsion in the integral homology of the quotient space, at prime numbers as high as for instance $p= 80\hspace{0.167em} 737$ at the discriminant $- 1747$.Supplementary materials are available with this article.

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41

AGAEV, SHAHIN S., ABDULLA I. MUKHTAROV, and YEGANA V. MAMEDOVA. "MESONS DISTRIBUTION AMPLITUDES IN THE "NAIVE NON-ABELIANIZATION" APPROXIMATION AND POWER-SUPPRESSED CORRECTIONS TO FM (Q2)." Modern Physics Letters A 15, no. 22n23 (July 30, 2000): 1419–28. http://dx.doi.org/10.1142/s0217732300001912.

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Power-suppressed corrections to the light pseudoscalar (π, K) and longitudinally polarized ρ-meson electromagnetic form factors FM (Q2) are estimated by means of the running coupling constant method. In calculating the mesons distribution amplitudes (DAs) found, the "naive non-abelianization" approximation is used. Comparisons are made with FM(Q2) obtained using the "ordinary" DAs and running coupling constant method, as well as with frozen coupling approximation's results.

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42

FERNÀNDEZ-VALÈNCIA, RAMSÈS, and JEFFREY GIANSIRACUSA. "ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS." Glasgow Mathematical Journal 60, no. 1 (February 7, 2017): 187–98. http://dx.doi.org/10.1017/s0017089516000653.

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AbstractWe study the homological algebra of bimodules over involutive associative algebras. We show that Braun's definition of involutive Hochschild cohomology in terms of the complex of involution-preserving derivations is indeed computing a derived functor: the ℤ/2-invariants intersected with the centre. We then introduce the corresponding involutive Hochschild homology theory and describe it as the derived functor of the pushout of ℤ/2-coinvariants and abelianization.

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43

Cencelj, M., and A. N. Dranishnikov. "Extension of Maps to Nilpotent Spaces." Canadian Mathematical Bulletin 44, no. 3 (September 1, 2001): 266–69. http://dx.doi.org/10.4153/cmb-2001-026-1.

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AbstractWe show that every compactum has cohomological dimension 1 with respect to a finitely generated nilpotent group G whenever it has cohomological dimension 1 with respect to the abelianization of G. This is applied to the extension theory to obtain a cohomological dimension theory condition for a finite-dimensional compactum X for extendability of every map from a closed subset of X into a nilpotent CW-complex M with finitely generated homotopy groups over all of X.

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44

DOKAS, IOANNIS. "TRIPLE COHOMOLOGY AND DIVIDED POWERS ALGEBRAS IN PRIME CHARACTERISTIC." Journal of the Australian Mathematical Society 87, no. 2 (October 2009): 161–73. http://dx.doi.org/10.1017/s1446788708081019.

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AbstractIn this paper using the Quillen–Barr–Beck (co-)homology theory of universal algebras we define (co-)homology groups for commutative algebras with divided powers in prime characteristic. In particular, we determine for A a commutative 𝔽p-algebra with divided powers, the category of Beck A-modules and the group of Beck derivations. We construct the abelianization functor and we define (co-)homology. Moreover, we determine the cohomology in low dimensions and we interpret the first cohomology in terms of extensions.

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45

Johnson, Dennis. "The structure of the Torelli group—III: The abelianization of I." Topology 24, no. 2 (1985): 127–44. http://dx.doi.org/10.1016/0040-9383(85)90050-3.

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46

Heller, Lynn, and Sebastian Heller. "Abelianization of Fuchsian systems on a $4$-punctured sphere and applications." Journal of Symplectic Geometry 14, no. 4 (2016): 1059–88. http://dx.doi.org/10.4310/jsg.2016.v14.n4.a4.

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47

Feigin, B. L. "Abelianization of the BGG resolution of representations of the Virasoro algebra." Functional Analysis and Its Applications 45, no. 4 (December 2011): 297–304. http://dx.doi.org/10.1007/s10688-011-0032-7.

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48

Elmouhib, Fouad, Mohamed Talbi, and Abdelmalek Azizi. "On some realizable metabelian 5-groups." Boletim da Sociedade Paranaense de Matemática 42 (April 19, 2024): 1–7. http://dx.doi.org/10.5269/bspm.62708.

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Let G be a 5-group of maximal class and G' = [G, G] its derived group. Assume that the abelianization G/G' is of type (5, 5) and the transfers from H1 to G' and from H2 to G' are trivial, where H1 and H2 are two maximal normal subgroups of G. Then G is completely determined with the isomorphism class groups of maximal class. Moreover the group G is realizable with some fields k, which is the normal closure of a pure quintic field.

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49

Putman, Andrew. "The Johnson homomorphism and its kernel." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 735 (February 1, 2018): 109–41. http://dx.doi.org/10.1515/crelle-2015-0017.

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AbstractWe give a new proof of a celebrated theorem of Dennis Johnson that asserts that the kernel of the Johnson homomorphism on the Torelli subgroup of the mapping class group is generated by separating twists. In fact, we prove a more general result that also applies to “subsurface Torelli groups”. Using this, we extend Johnson’s calculation of the rational abelianization of the Torelli group not only to the subsurface Torelli groups, but also to finite-index subgroups of the Torelli group that contain the kernel of the Johnson homomorphism.

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50

Azizi, Abdelmalek, Abdelkader Zekhnini, and Mohammed Taous. "On some metabelian 2-group and applications II." Boletim da Sociedade Paranaense de Matemática 34, no. 2 (June 29, 2015): 75–85. http://dx.doi.org/10.5269/bspm.v34i2.27016.

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Let G be some metabelian 2-group satisfying the condition G/G' is of type (2, 2, 2). In this paper, we construct all the subgroups of G of index 2 or 4, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem of the 2-ideal classes of some fields k satisfying the condition Gal(k_2^{(2)}/k) is isomorphic to G, where k_2^{(2)} is the second Hilbert 2-class field of k.

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