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Locally Finite Central Simple Algebras
Algebras and Representation Theory, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eliyahu Matzri, Uzi Vishne
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Central Simple Algebras and Galois Cohomology
, 2006 The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev–Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert, and the starting point of current research in motivic cohomology theory by ...
Philippe Gille, Tamás Szamuely
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Rational central simple algebras
Israel Journal of Mathematics, 1996Throughout, all central simple algebras are finite-dimensional over their centres, which in turn are finitely generated field extensions of a ground field \(k\), itself algebraically closed. By a torus of rank \(d\) the authors understand the algebraic group \(T=(k^*)^d\).
Zinovy Reichstein
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Efficient computations in central simple algebras using Amitsur cohomology
Journal of AlgebraWe introduce a presentation for central simple algebras over a field k using Amitsur cohomology. We provide efficient algorithms for computing a cocycle corresponding to any such algebra given by structure constants.
Peter Kutas, Mickael Montessinos
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Israel Journal of Mathematics, 1978
Wedderburn’s factorization of polynomials over division rings is refined and used to prove that every central division algebra of degree 8, with involution, has a maximal subfield which is a Galois extension of the center (with Galois group Z2⊕Z2⊕Z2). The same proof, for an arbitrary central division algebra of degree 4, gives an explicit construction ...
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Wedderburn’s factorization of polynomials over division rings is refined and used to prove that every central division algebra of degree 8, with involution, has a maximal subfield which is a Galois extension of the center (with Galois group Z2⊕Z2⊕Z2). The same proof, for an arbitrary central division algebra of degree 4, gives an explicit construction ...
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1994
The Wedderburn-Artin theorem reduces the study of semisimple algebras to the description of division algebras over a field K. If D is a finite dimensional division algebra over K and C its center, then C is a field (an extension of the field K) and D can be considered as an algebra over the field C.
Yurij A. Drozd, Vladimir V. Kirichenko
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The Wedderburn-Artin theorem reduces the study of semisimple algebras to the description of division algebras over a field K. If D is a finite dimensional division algebra over K and C its center, then C is a field (an extension of the field K) and D can be considered as an algebra over the field C.
Yurij A. Drozd, Vladimir V. Kirichenko
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1993
In the first two chapters we studied rings and modules. Many of the important examples we studied, such as polynomial rings, matrix rings, group rings and the quaternions, have additional structure we have been ignoring; namely, they are modules as well as rings, and the ring multiplication is compatible with the module multiplication.
Benson Farb, R. Keith Dennis
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In the first two chapters we studied rings and modules. Many of the important examples we studied, such as polynomial rings, matrix rings, group rings and the quaternions, have additional structure we have been ignoring; namely, they are modules as well as rings, and the ring multiplication is compatible with the module multiplication.
Benson Farb, R. Keith Dennis
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Construction of Central Simple Associative Algebras
The Annals of Mathematics, 1944The theory of crossed products is generalized to the case of a maximal subfield \(P\) of a central simple algebra \(\mathfrak A\) which is not necessarily galoisian over the ground field \(\Phi\). \(\mathfrak A\) is a double-module over \(P\) and defines a regular self-representation \(E\) of \(P\) [the author, Am. J. Math.
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Actions of Solvable Algebraic Groups on Central Simple Algebras
Algebras and Representation Theory, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Some Results on Central Simple Algebras
The Annals of Mathematics, 1956The present note is a continuation of the first part of [2].' The results of that part are applied here to obtain some new results on central simple algebras and some old ones in a new way. The first application is to the representation theory of the full linear group GL(n).
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