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Relevant bibliographies by topics / Torsion theory (algebra)

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Journal articles

Academic literature on the topic 'Torsion theory (algebra)'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 March 2023

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Journal articles on the topic "Torsion theory (algebra)"

1

PRICE, KENNETH L. "A DOMAIN TEST FOR LIE COLOR ALGEBRAS." Journal of Algebra and Its Applications 07, no. 01 (2008): 81–90. http://dx.doi.org/10.1142/s0219498808002679.

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Lie color algebras are generalizations of Lie superalgebras and graded Lie algebras. The properties of a Lie color algebra can often be related directly to the ring structure of its universal enveloping algebra. We study the effects of torsion elements and torsion subspaces. Let [Formula: see text] denote a Lie color algebra. If [Formula: see text] is homogeneous and torsion then x2 = 0 in [Formula: see text]. If no homogeneous element of [Formula: see text] is torsion, then [Formula: see text] so [Formula: see text] is semiprime. In this case we can give a test which uses Gröbner basis method

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2

Okoh, F. "Torsion-Free and Divisible Modules Over Finite-Dimensional Algebras." Canadian Mathematical Bulletin 39, no. 1 (1996): 111–14. http://dx.doi.org/10.4153/cmb-1996-014-9.

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AbstractIf R is a Dedekind domain, then div splits i.e.; the maximal divisible submodule of every R-module M is a direct summand of M. We investigate the status of this result for some finite-dimensional hereditary algebras. We use a torsion theory which permits the existence of torsion-free divisible modules for such algebras. Using this torsion theory we prove that the algebras obtained from extended Coxeter- Dynkin diagrams are the only such hereditary algebras for which div splits. The field of rational functions plays an essential role. The paper concludes with a new type of infinite-dime

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3

BARLAK, SELÇUK, TRON OMLAND, and NICOLAI STAMMEIER. "On the -theory of -algebras arising from integral dynamics." Ergodic Theory and Dynamical Systems 38, no. 3 (2016): 832–62. http://dx.doi.org/10.1017/etds.2016.63.

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We investigate the$K$-theory of unital UCT Kirchberg algebras${\mathcal{Q}}_{S}$arising from families$S$of relatively prime numbers. It is shown that$K_{\ast }({\mathcal{Q}}_{S})$is the direct sum of a free abelian group and a torsion group, each of which is realized by another distinct$C^{\ast }$-algebra naturally associated to$S$. The$C^{\ast }$-algebra representing the torsion part is identified with a natural subalgebra${\mathcal{A}}_{S}$of${\mathcal{Q}}_{S}$. For the$K$-theory of${\mathcal{Q}}_{S}$, the cardinality of$S$determines the free part and is also relevant for the torsion part, f

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4

Bland, Paul E. "Differential torsion theory." Journal of Pure and Applied Algebra 204, no. 1 (2006): 1–8. http://dx.doi.org/10.1016/j.jpaa.2005.03.005.

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Robertson, Guyan, and Tim Steger. "AsymptoticK-Theory for Groups Acting onÃ2Buildings." Canadian Journal of Mathematics 53, no. 4 (2001): 809–33. http://dx.doi.org/10.4153/cjm-2001-033-4.

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AbstractLet Γ be a torsion free lattice inG= PGL(3,) whereis a nonarchimedean local field. Then Γ acts freely on the affine Bruhat-Tits building ℬ ofGand there is an induced action on the boundary Ω of ℬ. The crossed productC*-algebra(Γ) =C(Ω) ⋊ Γ depends only on Γ and is classified by itsK-theory. This article shows how to compute theK-theory of(Γ) and of the larger class of rank two Cuntz-Krieger algebras.

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6

Kaufmann, Ralph M. "The algebra of discrete torsion." Journal of Algebra 282, no. 1 (2004): 232–59. http://dx.doi.org/10.1016/j.jalgebra.2004.07.042.

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7

Adachi, Takahide, Osamu Iyama, and Idun Reiten. "-tilting theory." Compositio Mathematica 150, no. 3 (2013): 415–52. http://dx.doi.org/10.1112/s0010437x13007422.

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AbstractThe aim of this paper is to introduce $\tau $-tilting theory, which ‘completes’ (classical) tilting theory from the viewpoint of mutation. It is well known in tilting theory that an almost complete tilting module for any finite-dimensional algebra over a field $k$ is a direct summand of exactly one or two tilting modules. An important property in cluster-tilting theory is that an almost complete cluster-tilting object in a 2-CY triangulated category is a direct summand of exactly two cluster-tilting objects. Reformulated for path algebras $kQ$, this says that an almost complete support

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8

TRUINI, P., and V. S. VARADARAJAN. "QUANTIZATION OF REDUCTIVE LIE ALGEBRAS: CONSTRUCTION AND UNIVERSALITY." Reviews in Mathematical Physics 05, no. 02 (1993): 363–415. http://dx.doi.org/10.1142/s0129055x93000103.

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The present paper addresses the question of universality of the quantization of reductive Lie algebras. Quantization is viewed as a torsion free deformation depending upon several parameters which are treated formally and not as complex numbers. The coalgebra and algebra structures are shown to restrict very sharply the possibilities for the infinite series in the generators of the Cartan subalgebra. Under an Ansatz which can be viewed as requiring that the two Borel subalgebras are deformed as Hopf algebras we construct a multi-parameter quantization which has the required property of univers

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9

Li, Hou Guo. "Application of Lie Group Analysis to the Plastic Torsion of Rod with the Saint Venant–Mises Yield Criterion." Advanced Materials Research 461 (February 2012): 265–71. http://dx.doi.org/10.4028/www.scientific.net/amr.461.265.

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Based on Lie group and Lie algebra theory, the basic principles of Lie group analysis of differential equations in mechanics are analyzed, and its validity in theory of plasticity is explained by example. For the plastic torsion of rod with variable cross section that consists in non-linear Saint Venant-Mises yield criterion, the 10-dimensional Lie algebra admitted by the equilibrium equation and yield criterion is completely solved, and invariants and group invariant solutions relative to different sub-algebras are given. At last, physical explanations of each group invariant solution are dis

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10

Colby, R. R., and K. R. Fuller. "Hereditary Torsion Theory Counter Equivalences." Journal of Algebra 183, no. 1 (1996): 217–30. http://dx.doi.org/10.1006/jabr.1996.0215.

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