Results 31 to 40 of about 11,773 (167)
Algebraic automorphism groups [PDF]
Illinois Journal of Mathematics, 1975 For an algebraic group G, let W(G) denote the group of all algebraic group automorphisms of G. In this chapter, we examine the possibility of endowing W(G) with the structure of an algebraic group in such a way that G becomes a strict W(G)-variety. The example of a toroid of dimension greater than 1 shows that this is not always possible. However, good
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Algebraic obstructions to sequential convergence in Hausdorrf abelian groups
International Journal of Mathematics and Mathematical Sciences, 1998 Given an abelian group G and a non-trivial sequence in G, when will it be possible to construct a Hausdroff topology on G that allows the sequence to converge?
Bradd Clark, Sharon Cates
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Algebraic (2, 2)-transformation groups [PDF]
Journal of Group Theory, 2009 This paper contains the more significant part of the article with the same title that will appear in the Volume 12 of Journal of Group Theory (2009). In this paper we determine all algebraic transformation groups $G$, defined over an algebraically closed field $\sf k$, which operate transitively, but not primitively, on a variety $ $, provided the ...
BARTOLONE, Claudio +2 more
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Group Algebras of Finite Groups as Lie Algebras [PDF]
Communications in Algebra, 2010 We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a decomposition in simple factors of these Lie algebras, in terms of the ordinary representations of $G$.
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Recent developments on the power graph of finite groups – a survey
AKCE International Journal of Graphs and Combinatorics, 2021 Algebraic graph theory is the study of the interplay between algebraic structures (both abstract as well as linear structures) and graph theory. Many concepts of abstract algebra have facilitated through the construction of graphs which are used as tools
Ajay Kumar +3 more
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Elekes-Szabó for groups, and approximate subgroups in weak general position
Discrete Analysis, 2023 Elekes-Szabó for groups, and approximate subgroups in weak general position, Discrete Analysis 2023:6, 28 pp. An important theorem of Elekes and Szabó shows that given an algebraic relation between triples of complex numbers (such as e.g.
Martin Bays +2 more
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Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups
Abstract and Applied Analysis, 2014 We obtain an analogue of Jørgensen's inequality in quaternionic hyperbolic space. As an application, we prove that if the r-generator quaternionic Kleinian group satisfies I-condition, then its algebraic limit is also a quaternionic Kleinian group.
Huani Qin, Yueping Jiang, Wensheng Cao
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THE GEOMETRY OF BLUEPRINTS PART II: TITS–WEYL MODELS OF ALGEBRAIC GROUPS
Forum of Mathematics, Sigma, 2018 This paper is dedicated to a problem raised by Jacquet Tits in 1956: the Weyl group of a Chevalley group should find an interpretation as a group over what is nowadays called $\mathbb{F}_{1}$, the field with one element.
OLIVER LORSCHEID
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ALGEBRAIC QUANTUM PERMUTATION GROUPS [PDF]
Asian-European Journal of Mathematics, 2008 We discuss some algebraic aspects of quantum permutation groups, working over arbitrary fields. If 𝕂 is any characteristic zero field, we show that there exists a universal cosemisimple Hopf algebra coacting on the diagonal algebra 𝕂n: this is a refinement of Wang's universality theorem for the (compact) quantum permutation group.
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A Tauberian Group Algebra [PDF]
Proceedings of the American Mathematical Society, 1973 Let G be the group of real matrices \[ ( x , y ) = ( e x
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