Two-dimensional real division algebras revisited.
Hübner, Marion, Petersson, Holger P. (2004)
Beiträge zur Algebra und Geometrie
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Hübner, Marion, Petersson, Holger P. (2004)
Beiträge zur Algebra und Geometrie
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Sergio Albeverio, Bakhrom A. Omirov, Isamiddin S. Rakhimov (2006)
Extracta Mathematicae
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Flaut, Cristina (2006)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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J. Monk (1993)
Banach Center Publications
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Jerzy Białkowski (2004)
Open Mathematics
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Ernst Dieterich (1999)
Colloquium Mathematicae
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Given a euclidean vector space V = (V,〈〉) and a linear map η: V ∧ V → V, the anti-commutative algebra (V,η) is called dissident in case η(v ∧ w) ∉ ℝv ⊕ ℝw for each pair of non-proportional vectors (v,w) ∈ . For any dissident algebra (V,η) and any linear form ξ: V ∧ V → ℝ, the vector space ℝ × V, endowed with the multiplication (α,v)(β,w) = (αβ -〈v,w〉+ ξ(v ∧ w), αw + βv + η(v ∧ w)), is a quadratic division algebra. Up to isomorphism, each real quadratic division algebra arises in this...
Jun, Young Bae, Kim, Hee Sik, Park, Chul Hwan (2011)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Yosuke Ohnuki, Kaoru Takeda, Kunio Yamagata (1999)
Colloquium Mathematicae
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By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule . We study the problem of when extension algebras of a K-algebra A are symmetric. (1) For an algebra A= KQ/I with an arbitrary finite quiver Q, we show a sufficient condition in terms of a 2-cocycle for an extension algebra to be symmetric. (2) Let L be a finite extension field of K. By using a given 2-cocycle of the K-algebra L, we construct a 2-cocycle of...
Jakubíková-Studenovská, Danica, Mašulović, Dragan, Pöschel, Reinhard (2004)
Beiträge zur Algebra und Geometrie
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Pelea, Cosmin (2008)
Acta Universitatis Apulensis. Mathematics - Informatics
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Ethier, Dillon, Lindberg, Tova, Luttman, Aaron (2010)
Annals of Functional Analysis (AFA) [electronic only]
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Jerzy Białkowski (2004)
Open Mathematics
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The Cartan matrix of a finite dimensional algebra A is an important combinatorial invariant reflecting frequently structural properties of the algebra and its module category. For example, one of the important features of the modular representation theory of finite groups is the nonsingularity of Cartan matrices of the associated group algebras (Brauer’s theorem). Recently, the class of all tame selfinjective algebras having simply connected Galois coverings and the stable Auslander-Reiten...