Results 41 to 50 of about 61,116 (180)
Loops embedded in generalized Cayley algebras of dimension 2r,r≥2
International Journal of Mathematics and Mathematical Sciences, 2001 Every Cayley algebra of dimension 2r,r≥2, contains an embedded invertible loop of order 2r+1 generated by its basis. Such a loop belongs to a class of non-abelian invertible loops that are flexible and power-associative.
Raoul E. Cawagas
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Symmetry, Integrability and Geometry: Methods and Applications, 2008 In this paper we prove that for any commutative (but in general non-associative) algebra A with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra V = V_0 oplus V2 oplus V3 oplus ..., such that dim V_0 = 1 and V_2 ...
Michael Roitman
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Poisson algebras in terms of non-associative algebras
Journal of Algebra, 2008 Let \(K\) be a field of characteristic different from 2 and 3. A Poisson algebra is a \(K\)-vector space \(P\) equipped with two bilinear operations: (1) a Lie bracket, referred to as a Poisson bracket, usually denoted by \(\{\;,\;\}\); (2) an associative commutative multiplication denoted by the authors by \(\bullet\).
Goze, Michel, Remm, Elisabeth
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Isotopic liftings of Clifford algebras and applications in elementary particle mass matrices
, 2007 Isotopic liftings of algebraic structures are investigated in the context of Clifford algebras, where it is defined a new product involving an arbitrary, but fixed, element of the Clifford algebra.
A.O.E. Animalu +28 more
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Hasse-Schmidt Derivations and the Hopf Algebra of Non-Commutative Symmetric Functions
Axioms, 2012 Let NSymm be the Hopf algebra of non-commutative symmetric functions (in an infinity of indeterminates): . It is shown that an associative algebra A with a Hasse-Schmidt derivation ) on it is exactly the same as an NSymm module algebra. The primitives of
Michiel Hazewinkel
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A standard form in (some) free fields: How to construct minimal linear representations
Open Mathematics, 2020 We describe a standard form for the elements in the universal field of fractions of free associative algebras (over a commutative field). It is a special version of the normal form provided by Cohn and Reutenauer and enables the use of linear algebra ...
Schrempf Konrad
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Determining When an Algebra Is an Evolution Algebra
Mathematics, 2020 Evolution algebras are non-associative algebras that describe non-Mendelian hereditary processes and have connections with many other areas. In this paper, we obtain necessary and sufficient conditions for a given algebra A to be an evolution algebra. We
Miguel D. Bustamante +2 more
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Non-associative algebras associated to Poisson algebras
, 2006 23 ...
Goze, Michel, Remm, Elisabeth
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Coagulation, non-associative algebras and binary trees
Physica D: Nonlinear Phenomena, 2023 We consider the classical Smoluchowski coagulation equation with a general frequency kernel. We show that there exists a natural deterministic solution expansion in the non-associative algebra generated by the convolution product of the coalescence term. The non-associative solution expansion is equivalently represented by binary trees.
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Automorphism Group of a Non-Associative Algebra I [PDF]
, 2008 Automorphisms of a Weyl-type non-associative subalgebra of WNn;m;s were studied in [2], [3], [4], [12], [13]. There are various papers on the automorphism groups of an associative algebra, a Lie algebra, and a non-associative algebra [4], [5], [11].
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