Results 51 to 60 of about 231,292 (124)
Irreducible highest weight representations of the simple n-Lie algebra [PDF]
, 2012 A. Dzhumadil’daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of all irreducible, highest weight modules, including the ...
Dana Bălibanu +5 more
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$K$-Theory of Azumaya algebras
Irish Mathematical Society Bulletin, 2010 For an Azumaya algebra $A$ which is free over its centre $R$, we prove that the $K$-theory of $A$ is isomorphic to $K$-theory of $R$ up to its rank torsion. We observe that a graded central simple algebra, graded by an abelian group, is a graded Azumaya algebra and it is free over its centre.
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The octonions form an Azumaya algebra in certain braided linear Gr-categories
, 2017 By applying the idea of viewing the octonions as an associative algebra in certain tensor categories, or more precisely as a twisted group algebra by a 2-cochain, we show that the octonions form an Azumaya algebra in some suitable braided linear Gr ...
Yang, Yuping +3 more
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Azumaya algebras with involutions
Journal of Algebra, 1990 Let R be a commutative ring and S/R an étale quadratic extension. Br(-) is the Brauer group and \({}_ 2Br(\)-) its 2-torsion. This paper studies the problem of when the sequence \[ _ 2Br(R)\quad \to^{Res}\quad_ 2Br(S)\quad \to^{Cores}\quad_ 2Br(R) \] is exact. If R, S are fields and char \(R\neq 2\), the sequence is known to be exact. From the authors'
Knus, M.-A, Parimala, R, Srinivas, V
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, 2012 This Saylor course is an extension of abstract algebra I and revisits structures like groups, rings and fields as well as mappings like homomorphisms and isomorphisms.
algebra, The Saylor Foundation
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, 2002 We define the notions of Azumaya category and Brauer group in category theory enriched over some very general base category V. We prove the equivalence of various definitions, in particular in terms of separable categories or progenerating bimodules ...
Borceux, Francis, Vitale, Enrico
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On an algebra associated to a ternary cubic curve
, 2014 In this paper we construct an algebra associated to a cubic curve C defined over a field F of characteristic not two or three. We prove that this algebra is an Azumaya algebra of rank nine.
Kuo, Jung-Miao
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Categorical Torelli theorems: results and open problems. [PDF]
Rend Circ Mat Palermo, 2023 Pertusi L, Stellari P.
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DIFFERENTIAL OPERATORS ON AZUMAYA ALGEBRAS AND HEISENBERG ALGEBRAS
Communications in Algebra, 2001 We use the definition of differential operators on noncommutative rings given by V.Lunts and A.Rosenberg to find the differential operators on Azumaya algebras and the Heisenberg algebras.
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A note on Azumaya algebras and one-forms
The crystalline differential operators on a smooth variety X give rise to a non-split Azumaya algebra over the cotangent bundle of the Frobenius ...
Siqing Zhang
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