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Open problems on central simple algebras [PDF]
Transformation Groups, 2011 v2 has some small revisions to the text.
Skip Garibaldi +2 more
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CHARACTERISTIC POLYNOMIALS OF CENTRAL SIMPLE ALGEBRAS
Taiwanese Journal of Mathematics, 2013 We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a central division algebra, and a description of separable conjugacy classes of the multiplicative group.
Chia-Fu Yu
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About Some Split Central Simple Algebras [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 In this paper we study certain quaternion algebras and symbol algebras which split.
Savin Diana
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Formally Real Involutions on Central Simple Algebras [PDF]
Communications in Algebra, 2008 An involution $#$ on an associative ring $R$ is \textit{formally real} if a sum of nonzero elements of the form $r^# r$ where $r \in R$ is nonzero. Suppose that $R$ is a central simple algebra (i.e. $R=M_n(D)$ for some integer $n$ and central division algebra $D$) and $#$ is an involution on $R$ of the form $r^# = a^{-1} r^\ast a$, where $\ast$ is some
Jakob Cimprič
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On the corestriction of central simple algebras
Mathematische Zeitschrift, 1987 This paper provides algebra-theoretic proofs for the following well-known results: (1) if L/K is a separable extension of fields of rank d and C is a central simple algebra over K, then \(cor_{L/K}(C\otimes L)\sim C^{\otimes d}\); (2) if L/K is a finite separable extension of fields and if a, b are non-zero elements of L and K respectively, then for ...
Jean-Pierre Tignol
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Tame group actions on central simple algebras
Journal of Algebra, 2007 We study actions of linear algebraic groups on finite-dimensional central simple algebras. We describe the fixed algebra for a broad class of such actions.
Reichstein, Z., Vonessen, N.
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A CHARACTERIZATION OF DERIVATIONS AND AUTOMORPHISMS ON SOME SIMPLE ALGEBRAS
Ural Mathematical Journal, 2022 In the present paper, we study simple algebras, which do not belong to the well-known classes of algebras (associative algebras, alternative algebras, Lie algebras, Jordan algebras, etc.).
Farhodjon Arzikulov +2 more
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Norms in central simple algebras [PDF]
Pacific Journal of Mathematics, 2018 Let A be a central simple algebra central over a number field K whose ring of integers is R. An outlier is an element r of R so that: r is a reduced norm of an element of A, but not the norm of an algebraic integer in A. We study properties and distribution of outliers.
Goldstein, Daniel, Schacher, Murray
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Algorithmic complexity of linear nonassociative algebra
Вестник КазНУ. Серия математика, механика, информатика, 2020 One of the central problems of algebraic complexity theory is the complexity of multiplication in algebras. For this, first, the concept of algebra is defined and the class of algebras under study is fixed.
R. K. Kerimbaev +2 more
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The “Defektsatz” for central simple algebras [PDF]
Transactions of the American Mathematical Society, 1992 Let Q Q be a central simple algebra finite-dimensional over its center
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