Results 1 to 10 of about 178 (174)
Division algebras of degree 4 and 8 with involution [PDF]
Israel Journal of Mathematics, 1979 We develop necessary and sufficient conditions for central simple algebras to have involutions of the first kind, and to be tensor products of quaternion subalgebras. The theory is then applied to give an example of a division algebra of degree 8 with involution (of the first kind), without quaternion subalgebras, answering an old question of Albert ...
Amitsur, S. A. +2 more
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On Division Algebras of Degree 3 with Involution
Journal of Algebra, 1996 The authors present a simple proof of the theorem [\textit{A. A. Albert}, Scripta Math. 26, 309-316 (1963; Zbl 0147.28702)] that a division algebra of degree 3 (in characteristic not 3) with an involution \(J\) of the second kind has a maximal subfield which is Galois over the fixed field of \(J\), with the symmetric group of degree 3 as Galois group ...
Darrell E Haile, Max-Albert Knus
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Decomposition of Mal'cev-Neumann division algebras with involution
Mathematische Zeitschrift, 1994 See the review in Zbl 0812.16023.
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Division algebras with an anti-automorphism but with no involution [PDF]
advg, 2005 The authors construct interesting examples of division rings having an anti-automorphism but no involutions. The problem stems from projective geometry. It is classical that if \(D\) is a division ring and \(V\) a finite dimensional right \(D\)-vector space of dimension at least 3, then the projective space \(P(V)\) has a duality (resp.
Morandi, P. J. +2 more
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Discriminants of involutions on Henselian division algebras [PDF]
Pacific Journal of Mathematics, 1995 The purpose of this paper is to compute the discriminant of an involution of the first kind on a finite dimensional division algebra over a field with a Henselian valuation of residual characteristic different from 2 in terms of residue information. The results depend on the kind of residue involution and on whether the division algebra is inertially ...
Chacron, M. +4 more
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Free algebras in division rings with an involution [PDF]
Journal of Algebra, 2018 11 ...
Ferreira, Vitor O. +2 more
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Decomposition of involutions on inertially split division algebras [PDF]
Mathematische Zeitschrift, 2000 Let \(F\) be a Henselian valued field with residue field \(\overline F\) of characteristic not~\(2\) and let \(S\) be an \(F\)-central (finite-dimensional) division algebra which is split by an inertial extension of \(F\). Assume \(\sigma\) is an involution on \(S\) (i.e., an anti-automorphism of period~\(2\)) which is the identity on an inertial lift ...
Morandi, P. J., Sethuraman, B. A.
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Classification of involutions on graded-division simple real algebras [PDF]
Linear Algebra and its Applications, 2018 29 pages, 2 figures. This is the accepted manuscript (accommodating the referee's suggestions) of the article published in Linear Algebra and its ...
Yuri Bahturin +2 more
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Homogeneous involutions on graded division algebras and their polynomial identities
Journal of Algebra and Its Applications, 2023 In this paper, we describe the so-called homogeneous involution on finite-dimensional graded-division algebra over an algebraically closed field. We also compute their graded polynomial identities with involution. As pointed out by Fonseca and Mello, a homogeneous involution naturally appears when dealing with graded polynomial identities and a ...
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A note on Clifford algebras and central division algebras with involution [PDF]
Glasgow Mathematical Journal, 1985 In this note we consider the question as to which central division algebras occur as the Clifford algebra of a quadratic form over a field. Non-commutative ones other than quaternion division algebras can occur and it is also the case that there are certain central division algebras D which, while not themselves occurring as a Clifford algebra, are ...
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