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Journal articles on the topic 'Birman-Murakami-Wenzl algebras'

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Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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1

Häring-Oldenburg, Reinhard. "Cyclotomic Birman–Murakami–Wenzl algebras." Journal of Pure and Applied Algebra 161, no. 1-2 (July 2001): 113–44. http://dx.doi.org/10.1016/s0022-4049(00)00100-6.

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2

Goodman, Frederick M. "Cellularity of cyclotomic Birman–Wenzl–Murakami algebras." Journal of Algebra 321, no. 11 (June 2009): 3299–320. http://dx.doi.org/10.1016/j.jalgebra.2008.05.017.

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3

Rui, Hebing, and Linliang Song. "Decomposition matrices of Birman–Murakami–Wenzl algebras." Journal of Algebra 444 (December 2015): 246–71. http://dx.doi.org/10.1016/j.jalgebra.2015.07.033.

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4

GOODMAN, FREDERICK M., and HOLLY HAUSCHILD MOSLEY. "CYCLOTOMIC BIRMAN–WENZL–MURAKAMI ALGEBRAS, I: FREENESS AND REALIZATION AS TANGLE ALGEBRAS." Journal of Knot Theory and Its Ramifications 18, no. 08 (August 2009): 1089–127. http://dx.doi.org/10.1142/s0218216509007397.

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The cyclotomic Birman–Wenzl–Murakami algebras are quotients of the affine BMW algebras in which the affine generator satisfies a polynomial relation. We show that the cyclotomic BMW algebras are free modules over any admissible, integral ground ring, and that they are isomorphic to cyclotomic versions of the Kauffman tangle algebras.

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5

Cohen, Arjeh M., Dié A. H. Gijsbers, and David B. Wales. "The Birman–Murakami–Wenzl Algebras of Type Dn." Communications in Algebra 42, no. 1 (October 18, 2013): 22–55. http://dx.doi.org/10.1080/00927872.2012.678955.

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6

Isaev, A. P., and O. V. Ogievetsky. "Jucys-Murphy elements for Birman-Murakami-Wenzl algebras." Physics of Particles and Nuclei Letters 8, no. 3 (May 2011): 234–43. http://dx.doi.org/10.1134/s1547477111030125.

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7

Hu, Jun, and Zhankui Xiao. "On tensor spaces for Birman–Murakami–Wenzl algebras." Journal of Algebra 324, no. 10 (November 2010): 2893–922. http://dx.doi.org/10.1016/j.jalgebra.2010.08.017.

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8

Xu, Xu. "The Structure of Simple Modules of Birman-Murakami-Wenzl Algebras." Journal of Mathematics 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/876251.

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We study the restriction of simple modulesDf,λof Birman-Murakami-Wenzl algebrasBn(r,q)withq being not a root of 1. Precisely, we study the module structure for the restriction ofDf,λtoBn-1(r,q)and describe the socle and head of the restriction of each simple module completely.

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9

Cohen, Arjeh M., and David B. Wales. "The Birman-Murakami-Wenzl algebras of type E n." Transformation Groups 16, no. 3 (June 17, 2011): 681–715. http://dx.doi.org/10.1007/s00031-011-9150-9.

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10

Isaev, A. P., A. I. Molev, and O. V. Ogievetsky. "Idempotents for Birman-Murakami-Wenzl algebras and reflection equation." Advances in Theoretical and Mathematical Physics 18, no. 1 (2014): 1–25. http://dx.doi.org/10.4310/atmp.2014.v18.n1.a1.

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11

Beliakova, Anna, and Christian Blanchet. "Skein construction of idempotents in Birman-Murakami-Wenzl algebras." Mathematische Annalen 321, no. 2 (October 1, 2001): 347–73. http://dx.doi.org/10.1007/s002080100233.

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12

Rui, Hebing, and Mei Si. "Non-vanishing Gram determinants for cyclotomic Nazarov–Wenzl and Birman–Murakami–Wenzl algebras." Journal of Algebra 335, no. 1 (June 2011): 188–219. http://dx.doi.org/10.1016/j.jalgebra.2011.03.016.

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13

Wilcox, S., and S. Yu. "On the cellularity of the cyclotomic Birman-Murakami-Wenzl algebras." Journal of the London Mathematical Society 86, no. 3 (September 11, 2012): 911–29. http://dx.doi.org/10.1112/jlms/jds019.

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14

Enyang, John. "Cellular bases for the Brauer and Birman–Murakami–Wenzl algebras." Journal of Algebra 281, no. 2 (November 2004): 413–49. http://dx.doi.org/10.1016/j.jalgebra.2003.03.002.

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15

Goodman, Frederick M. "Comparison of admissibility conditions for cyclotomic Birman–Wenzl–Murakami algebras." Journal of Pure and Applied Algebra 214, no. 11 (November 2010): 2009–16. http://dx.doi.org/10.1016/j.jpaa.2010.02.005.

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16

Goodman, Frederick M., and Holly Hauschild Mosley. "Cyclotomic Birman–Wenzl–Murakami Algebras, II: Admissibility Relations and Freeness." Algebras and Representation Theory 14, no. 1 (December 11, 2009): 1–39. http://dx.doi.org/10.1007/s10468-009-9173-2.

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17

Goodman, Frederick M., and Holly Hauschild. "Affine Birman–Wenzl–Murakami algebras and tangles in the solid torus." Fundamenta Mathematicae 190 (2006): 77–137. http://dx.doi.org/10.4064/fm190-0-4.

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18

COHEN, ARJEH M., DIÉ A. H. GIJSBERS, and DAVID B. WALES. "TANGLE AND BRAUER DIAGRAM ALGEBRAS OF TYPE Dn." Journal of Knot Theory and Its Ramifications 18, no. 04 (April 2009): 447–83. http://dx.doi.org/10.1142/s0218216509007063.

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A generalization of the Kauffman tangle algebra is given for Coxeter type D n. The tangles involve a pole of order 2. The algebra is shown to be isomorphic to the Birman–Murakami–Wenzl algebra of the same type. This result extends the isomorphism between the two algebras in the classical case, which, in our set-up, occurs when the Coxeter type is A n - 1. The proof involves a diagrammatic version of the Brauer algebra of type D n of which the generalized Temperley–Lieb algebra of type D n is a subalgebra.

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19

Enyang, John. "Specht modules and semisimplicity criteria for Brauer and Birman–Murakami–Wenzl algebras." Journal of Algebraic Combinatorics 26, no. 3 (April 7, 2007): 291–341. http://dx.doi.org/10.1007/s10801-007-0058-3.

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20

DIPPER, RICHARD, JUN HU, and FRIEDERIKE STOLL. "SYMMETRIZERS AND ANTISYMMETRIZERS FOR THE BMW-ALGEBRA." Journal of Algebra and Its Applications 12, no. 07 (May 16, 2013): 1350032. http://dx.doi.org/10.1142/s0219498813500321.

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Let n ∈ ℕ and Bn(r, q) be the generic Birman–Murakami–Wenzl algebra with respect to indeterminants r and q. It is known that Bn(r, q) has two distinct linear representations generated by two central elements of Bn(r, q) called the symmetrizer and antisymmetrizer of Bn(r, q). These generate for n ≥ 3 the only one-dimensional two sided ideals of Bn(r, q) and generalize the corresponding notion for Hecke algebras of type A. The main result, Theorem 3.1, in this paper explicitly determines the coefficients of these elements with respect to the graphical basis of Bn(r, q).

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21

Isaev, A. P., A. N. Kirillov, and V. O. Tarasov. "Bethe subalgebras in affine Birman–Murakami–Wenzl algebras and flat connections for q-KZ equations." Journal of Physics A: Mathematical and Theoretical 49, no. 20 (April 18, 2016): 204002. http://dx.doi.org/10.1088/1751-8113/49/20/204002.

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22

Marin, Ivan. "Braids inside the Birman–Wenzl–Murakami algebra." Algebraic & Geometric Topology 10, no. 4 (September 9, 2010): 1865–86. http://dx.doi.org/10.2140/agt.2010.10.1865.

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23

Zhou, Cheng-Cheng, Kang Xue, Gang-Cheng Wang, Chun-Fang Sun, and Gui-Jiao Du. "Birman—Wenzl—Murakami Algebra and Topological Basis." Communications in Theoretical Physics 57, no. 2 (February 2012): 179–82. http://dx.doi.org/10.1088/0253-6102/57/2/02.

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24

Rui, Hebing, and Mei Si. "Singular parameters for the Birman–Murakami–Wenzl algebra." Journal of Pure and Applied Algebra 216, no. 6 (June 2012): 1295–305. http://dx.doi.org/10.1016/j.jpaa.2011.10.039.

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25

Pasquier, Vincent. "Incompressible Representations of the Birman-Wenzl-Murakami Algebra." Annales Henri Poincaré 7, no. 4 (April 25, 2006): 603–19. http://dx.doi.org/10.1007/s00023-006-0262-z.

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26

Kulish, P. P., N. Manojlović, and Z. Nagy. "Symmetries of spin systems and Birman–Wenzl–Murakami algebra." Journal of Mathematical Physics 51, no. 4 (April 2010): 043516. http://dx.doi.org/10.1063/1.3366259.

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27

Zhou, Chengcheng, Kang Xue, Lidan Gou, Chunfang Sun, Gangcheng Wang, and Taotao Hu. "Birman–Wenzl–Murakami algebra, topological parameter and Berry phase." Quantum Information Processing 11, no. 6 (November 16, 2011): 1765–73. http://dx.doi.org/10.1007/s11128-011-0331-1.

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28

Grimm, Uwe. "TrigonometricR matrices related to ?dilute? Birman-Wenzl-Murakami algebra." Letters in Mathematical Physics 32, no. 3 (November 1994): 183–87. http://dx.doi.org/10.1007/bf00750661.

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29

GOU, LIDAN, KANG XUE, QINGYONG WANG, GANGCHENG WANG, and CHUNFANG SUN. "A REPRESENTATION OF SPECIALIZED BIRMAN-WENZL-MURAKAMI ALGEBRA AND BERRY PHASE IN YANG-BAXTER SYSTEM." International Journal of Quantum Information 08, no. 07 (October 2010): 1187–97. http://dx.doi.org/10.1142/s0219749910006320.

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We present an S-matrix, a solution of the braid relation. A matrix representation of specialized Birman-Wenzl-Murakami algebra is obtained. Based on which, a unitary [Formula: see text]-matrix is generated via the Yang-Baxterization approach. Then we construct a Yang-Baxter Hamiltonian through the unitary [Formula: see text]-matrix. Berry phase of this Yang-Baxter system is investigated in detail.

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30

Grimm, U. "Dilute Birman-Wenzl-Murakami algebra and Dn+1(2) models." Journal of Physics A: Mathematical and General 27, no. 17 (September 7, 1994): 5897–905. http://dx.doi.org/10.1088/0305-4470/27/17/022.

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31

Belavin, Vladimir, and Doron Gepner. "Three blocks solvable lattice models and Birman–Murakami–Wenzl algebra." Nuclear Physics B 938 (January 2019): 223–31. http://dx.doi.org/10.1016/j.nuclphysb.2018.11.009.

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32

Liu, Bo, Kang Xue, Gangcheng Wang, Ying Liu, and Chunfang Sun. "Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model." International Journal of Quantum Information 13, no. 03 (April 2015): 1550017. http://dx.doi.org/10.1142/s0219749915500173.

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In this paper, we study three-dimensional (3D) reduced Birman–Murakami–Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.

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33

MacKay, N. J. "The fusion of R‐matrices using the Birman–Wenzl–Murakami algebra." Journal of Mathematical Physics 33, no. 4 (April 1992): 1529–37. http://dx.doi.org/10.1063/1.529677.

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34

BLUMEN, SACHA C. "ON THE Uq(osp(1|2n)) AND U-q(so(2n + 1)) UNCOLORED QUANTUM LINK INVARIANTS." Journal of Knot Theory and Its Ramifications 19, no. 03 (March 2010): 335–53. http://dx.doi.org/10.1142/s0218216510007851.

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Let L be a link and [Formula: see text] its link invariant associated with the vector representation of the quantum (super)algebra Uq(A). Let FL(r, s) be the Kauffman link invariant for L associated with the Birman–Wenzl–Murakami algebra BWMf(r, s) for complex parameters r and s and a sufficiently large rank f. For an arbitrary link L, we show that [Formula: see text] and [Formula: see text] for each positive integer n and all sufficiently large f, and that [Formula: see text] and [Formula: see text] are identical up to a substitution of variables. For at least one class of links FL(-r, -s) = FL(r, s) implying [Formula: see text] for these links.

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35

Gou, Li-Dan, Kang Xue, and Gang-Cheng Wang. "A 9 × 9 Matrix Representation of Birman—Wenzl—Murakami Algebra and Berry Phase in Yang—Baxter System." Communications in Theoretical Physics 55, no. 2 (February 2011): 263–67. http://dx.doi.org/10.1088/0253-6102/55/2/14.

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36

Rui, H., and M. Si. "Blocks of Birman-Murakami-Wenzl Algebras." International Mathematics Research Notices, April 30, 2010. http://dx.doi.org/10.1093/imrn/rnq083.

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37

Crampé, Nicolas, Luc Vinet, and Meri Zaimi. "Temperley–Lieb, Birman–Murakami–Wenzl and Askey–Wilson Algebras and Other Centralizers of $$U_q(\mathfrak {sl}_2)$$." Annales Henri Poincaré, June 6, 2021. http://dx.doi.org/10.1007/s00023-021-01064-x.

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38

Zhang, Kun, and Yong Zhang. "Quantum teleportation and Birman–Murakami–Wenzl algebra." Quantum Information Processing 16, no. 2 (January 17, 2017). http://dx.doi.org/10.1007/s11128-016-1512-8.

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