Download Algebras, Representations and Applications: Conference in by Vyacheslav Futorny, Victor Kac, Iryna Kashuba, Efim Zelmanov PDF

By Vyacheslav Futorny, Victor Kac, Iryna Kashuba, Efim Zelmanov

This quantity includes contributions from the convention on 'Algebras, Representations and purposes' (Maresias, Brazil, August 26 - September 1, 2007), in honor of Ivan Shestakov's sixtieth birthday. This publication might be of curiosity to graduate scholars and researchers operating within the thought of Lie and Jordan algebras and superalgebras and their representations, Hopf algebras, Poisson algebras, Quantum teams, crew earrings and different subject matters

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Hence H H8 . 6 is not satisfied and H is not cocommutative. Finally it is necessary to mention that S. 13. 2 by a (skew-)symmetric matrix U and by an irreducible projective representation g → Ag of the group G. 2] H is uniquely determined by the representation up to an orthogonal equivalence for U = E and up to a symplectic equivalence if U = S of representations. 13. 13. 6] the order of the group G(H) of group-like elements in H does not exceed 3n and if G is Abelian then |G(H)| 2n. 2 is not a group algebra.

Gn D} where g1 = 1. Then V has a base e1 = e, e2 = Ψ(g2 )e, . . 7) where Ψ(d)e = χ(d)e, d ∈ D, with some one-dimensional character χ of D. 8. If d ∈ D then Ψ(d)em = χ(d)χ([d, gm ])em for any m. Proof. Since (G∗ ) ⊆ D for any d ∈ D we obtain −1 Ψ(d)em = Ψ(d)Ψ(gm )e = Ψ(gm )Ψ(d)Ψ([d−1 , gm ])e = Ψ(gm )Ψ(d)Ψ([d, gm ])e = χ(d)χ([d, gm ])Ψ(gm )e = χ(d)χ([d, gm ])em for any d ∈ D. 9. 7) ⎛ ⎞ 1 0 ... 0 ⎜0 χ([d, g2 ]) . . ⎟ 0 ⎟ Ψ(d) = χ(d) ⎜ ⎝. . . . . . . . . . . . . . ⎠ . 0 0 . . χ([d, gn ]) In particular tr Ψ(d) = χ(d) ( n m=1 χ([d, gm ])).

Any Akivis superalgebra, defined over a field of characteristic different from 2 and 3, is special. 6. BIBLIOGRAPHY [1] Akivis M. , ”Local algebras of a multidimensional three web” (Russian), Sibirsk. Mat. Zh. 17 (1), (1976) 5-11; [2] Albuquerque H. , A. Elduque and Jos´e P´erez-Izquierdo, ”Z2 - quasialgebras”, Comm. , ”Algebras, hyperalgebras, nonassociative bialgebras and loops”, Advances in Mathematics 208, (2007) 834-876; [5] P´erez-Izquierdo J. , ”An envelope for Malcev algebras”, J. , ”Every Akivis Algebra is Linear”, Geometriae Dedicata 77 (2), (1999) 215-223; [7] Shestakov I.

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