Relevant bibliographies by topics / Just infinite Lie rings

Academic literature on the topic 'Just infinite Lie rings'

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Published: 10 March 2023

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Journal articles on the topic "Just infinite Lie rings"

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Bell, Jason, John Farina, and Cayley Pendergrass-Rice. "Stably just infinite rings." Journal of Algebra 319, no. 6 (March 2008): 2533–44. http://dx.doi.org/10.1016/j.jalgebra.2007.08.011.

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de Morais Costa, Otto Augusto, and Victor Petrogradsky. "Fractal just infinite nil Lie superalgebra of finite width." Journal of Algebra 504 (June 2018): 291–335. http://dx.doi.org/10.1016/j.jalgebra.2018.02.014.

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Voll, Christopher. "IDEAL ZETA FUNCTIONS ASSOCIATED TO A FAMILY OF CLASS-2-NILPOTENT LIE RINGS." Quarterly Journal of Mathematics 71, no. 3 (June 17, 2020): 959–80. http://dx.doi.org/10.1093/qmathj/haaa010.

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Abstract We produce explicit formulae for various ideal zeta functions associated to the members of an infinite family of class-$2$-nilpotent Lie rings, introduced in M. N. Berman, B. Klopsch and U. Onn (A family of class-2 nilpotent groups, their automorphisms and pro-isomorphic zeta functions, Math. Z. 290 (2018), 909935), in terms of Igusa functions. As corollaries we obtain information about analytic properties of global ideal zeta functions, local functional equations, topological, reduced and graded ideal zeta functions, as well as representation zeta functions for the unipotent group schemes associated to the Lie rings in question.
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4

Humphries, Stephen P. "Braid groups, infinite Lie algebras of Cartan type and rings of invariants." Topology and its Applications 95, no. 3 (August 1999): 173–205. http://dx.doi.org/10.1016/s0166-8641(98)00007-8.

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Weigel, Thomas. "On the Rigidity of Lie Lattices and Just Infinite Powerful Groups." Journal of the London Mathematical Society 62, no. 2 (October 2000): 381–97. http://dx.doi.org/10.1112/s0024610700001204.

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6

Smoktunowicz, Agata. "On Primitive Ideals in Graded Rings." Canadian Mathematical Bulletin 51, no. 3 (September 1, 2008): 460–66. http://dx.doi.org/10.4153/cmb-2008-046-1.

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AbstractLet R = be a graded nil ring. It is shown that primitive ideals in R are homogeneous. Let A = be a graded non-PI just-infinite dimensional algebra and let I be a prime ideal in A. It is shown that either I = ﹛0﹜ or I = A. Moreover, A is either primitive or Jacobson radical.
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Leary, I. J. "The integral cohomology rings of some p-groups." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 1 (July 1991): 25–32. http://dx.doi.org/10.1017/s0305004100070080.

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We determine the integral cohomology rings of an infinite family of p-groups, for odd primes p, with cyclic derived subgroups. Our method involves embedding the groups in a compact Lie group of dimension one, and was suggested independently by P. H. Kropholler and J. Huebschmann. This construction has also been used by the author to calculate the mod-p cohomology of the same groups and by B. Moselle to obtain partial results concerning the mod-p cohomology of the extra special p-groups [7], [9].
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8

Zhang, Zhi-Yong. "Symmetry determination and nonlinearization of a nonlinear time-fractional partial differential equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2233 (January 2020): 20190564. http://dx.doi.org/10.1098/rspa.2019.0564.

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We first show that the infinitesimal generator of Lie symmetry of a time-fractional partial differential equation (PDE) takes a unified and simple form, and then separate the Lie symmetry condition into two distinct parts, where one is a linear time-fractional PDE and the other is an integer-order PDE that dominates the leading position, even completely determining the symmetry for a particular type of time-fractional PDE. Moreover, we show that a linear time-fractional PDE always admits an infinite-dimensional Lie algebra of an infinitesimal generator, just as the case for a linear PDE and a nonlinear time-fractional PDE admits, at most, finite-dimensional Lie algebra. Thus, there exists no invertible mapping that converts a nonlinear time-fractional PDE to a linear one. We illustrate the results by considering two examples.
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9

MAL'CEV, YURI N. "JUST NON COMMUTATIVE VARIETIES OF OPERATOR ALGEBRAS AND RINGS WITH SOME CONDITIONS ON NILPOTENT ELEMENTS." Tamkang Journal of Mathematics 27, no. 1 (March 1, 1996): 59–65. http://dx.doi.org/10.5556/j.tkjm.27.1996.4362.

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In §1 it is given a classification of Just noncommutative varieties of associative over algebras over commutative Jacobson ring with unity. In [1], [4] are given different proofs of the commutativity of a finite ring with central nilpotent elements. In §2 we give generalizations of these results for infinite rings and for the case of Engel identity.
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10

Hartl, Manfred. "A Universal Coefficient Decomposition for Subgroups Induced by Submodules of Group Algebras." Canadian Mathematical Bulletin 40, no. 1 (March 1, 1997): 47–53. http://dx.doi.org/10.4153/cmb-1997-005-0.

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AbstractDimension subgroups and Lie dimension subgroups are known to satisfy a ‘universal coefficient decomposition’, i.e. their value with respect to an arbitrary coefficient ring can be described in terms of their values with respect to the ‘universal’ coefficient rings given by the cyclic groups of infinite and prime power order. Here this fact is generalized to much more general types of induced subgroups, notably covering Fox subgroups and relative dimension subgroups with respect to group algebra filtrations induced by arbitrary N-series, as well as certain common generalisations of these which occur in the study of the former. This result relies on an extension of the principal universal coefficient decomposition theorem on polynomial ideals (due to Passi, Parmenter and Seghal), to all additive subgroups of group rings. This is possible by using homological instead of ring theoretical methods.
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Dissertations / Theses on the topic "Just infinite Lie rings"

1

Gontcharov, Aleksandr. "On the Conjugacy of Maximal Toral Subalgebras of Certain Infinite-Dimensional Lie Algebras." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/26086.

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We will extend the conjugacy problem of maximal toral subalgebras for Lie algebras of the form $\g{g} \otimes_k R$ by considering $R=k[t,t^{-1}]$ and $R=k[t,t^{-1},(t-1)^{-1}]$, where $k$ is an algebraically closed field of characteristic zero and $\g{g}$ is a direct limit Lie algebra. In the process, we study properties of infinite matrices with entries in a B\'zout domain and we also look at how our conjugacy results extend to universal central extensions of the suitable direct limit Lie algebras.
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Ziani, Dario Villanis. "Just infinite profinite structures." Doctoral thesis, 2021. http://hdl.handle.net/2158/1239059.

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In this thesis we show some new examples of just infinite profinite groups which are not pro-p groups. Moreover, we outline some characterization theorems for other profinite just infinite structures, such as residually solvable Lie algebras. Finally, we establish some results about profinite Noetherian groups.
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Books on the topic "Just infinite Lie rings"

1

Differential geometry, Lie groups, and symmetric spaces over general base fields and rings. Providence, R.I: American Mathematical Society, 2008.

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2

Neher, Erhard. Geometric representation theory and extended affine Lie algebras. Providence, R.I: American Mathematical Society, 2011.

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Geometric representation theory and extended affine Lie algebras. Providence, R.I: American Mathematical Society, 2011.

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4

Lie algebras, lie superalgebras, vertex algebras, and related topics: Southeastern Lie Theory Workshop Series 2012-2014 : Categorification of Quantum Groups and Representation Theory, April 21-22, 2012, North Carolina State University : Lie Algebras, Vertex Algebras, Integrable Systems and Applications, December 16-18, 2012, College of Charleston : Noncommutative Algebraic Geometry and Representation Theory, May 10-12, 2013, Louisiana State Vniversity : Representation Theory of Lie Algebras and Lie Superalgebras, May 16-17, 2014, University of Georgia. Providence, Rhode Island: American Mathematical Society, 2016.

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1943-, Seitz Gary M., ed. Unipotent and nilpotent classes in simple algebraic groups and lie algebras. Providence, R.I: American Mathematical Society, 2012.

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6

Southeastern Lie Theory Workshop on Combinatorial Lie Theory and Applications (2009 : North Carolina State University), Southeastern Lie Theory Conference on Homological Methods in Representation Theory (2010 : University of Georgia), and Southeastern Lie Theory Workshop: Finite and Algebraic Groups (2011 : University of Virginia), eds. Recent developments in Lie algebras, groups, and representation theory: 2009-2011 Southeastern Lie Theory Workshop series : Combinatorial Lie Theory and Applications, October 9-11, 2009, North Carolina State University : Homological Methods in Representation Theory, May 22-24, 2010, University of Georgia : Finite and Algebraic Groups, June 1-4, 2011, University of Virginia. Providence, Rhode Island: American Mathematical Society, 2012.

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Representation theory and mathematical physics: Conference in honor of Gregg Zuckerman's 60th birthday, October 24--27, 2009, Yale University. Providence, R.I: American Mathematical Society, 2011.

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Polcino, Milies César, ed. Groups, algebras and applications: XVIII Latin American Algebra Colloquium, August 3-8, 2009, São Pedro, SP, Brazil. Providence, R.I: American Mathematical Society, 2011.

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Noncommutative geometry and global analysis: Conference in honor of Henri Moscovici, June 29-July 4, 2009, Bonn, Germany. Providence, R.I: American Mathematical Society, 2011.

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1932-, Bass Hyman, and Lam, T. Y. (Tsit-Yuen), 1942-, eds. Algebra. Providence, R.I: American Mathematical Society, 2010.

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Book chapters on the topic "Just infinite Lie rings"

1

"Just infinite periodic Lie algebras." In Finite Groups 2003, 73–86. De Gruyter, 2004. http://dx.doi.org/10.1515/9783110198126.73.

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Dahlberg, Randall P. "Infinite Extensions of Simple Modules over Semisimple Lie Algebras." In Rings, extensions, and cohomology, 67–86. CRC Press, 2020. http://dx.doi.org/10.1201/9781003071815-7.

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Kurdachenko, L. A., A. A. Pypka, and I. Ya Subbotin. "On New Analogs of Some Classical Group Theoretical Results in Lie Rings." In Infinite Group Theory, 197–213. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813204058_0011.

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Zalasiewicz, Jan. "Tectonic Escalator." In The Earth After Us. Oxford University Press, 2008. http://dx.doi.org/10.1093/oso/9780199214976.003.0009.

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How does it work, this engine that produces the world’s strata, those storehouses of an almost infinite history? Our future explorers might be sorely puzzled, for the Earth’s motor is quite specific in its mechanism. There is nothing else like it in the solar system, and even reasonably close duplicates of it may be rare among planetary systems generally. A problem is immediately encountered in any attempt to construct a history of the Earth’s life and environments from the stratal archives. For the question will extend beyond simply explaining why the strata that formed on ancient sea floors happen to be present high up on land. Any explorer, in trying to construct a coherent history of the Earth, will find anything but coherence in those rock layers, once they try to put them back into their original order. For in many regions of the earth the strata are tilted, or are upside down, or are crumpled into huge folds, or have been sliced into segments in which the primary stratal layers are markedly off set from one another. Some layers show signs of having been recrystallized by heat and pressure, showing that they must have somehow been carried down to great depths below the Earth’s surface, and then carried back up again to lie exposed at the surface. The strata of neighbouring Mars, by contrast, have nothing like the richness of the Earth’s—but neither do they possess such formidable structural complications. These crazy Earthly stratal geometries, just as much as earthquakes or volcanoes, are indisputable signs of an active planet, in which the seemingly solid and stable crustal surface is, in reality, highly mobile. Our future explorers should take it for granted that strata are essentially made of sediment that was eroded from topographic highs (say, mountains) and was carried down to topographic lows (say, the floor of a lake or of a deep sea). This is straightforward. It has happened, say, on Mars. But on Mars it essentially happened as one cycle, a long time ago, where the highlands represent the eroded areas and the flatlands are an accumulation of the sediment derived from them.
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