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Jornal de Teoria Generalizada de Mentiras e Aplicações

Volume 2, Emitir 2 (2008)

Artigo de Pesquisa

Enveloping algebras of Hom-Lie algebras

Donald YAU

Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed. 2000 MSC: 05C05, 17A30, 17A32, 17A50, 17B01, 17B35, 17D25 1

Artigo de Pesquisa

Classical elliptic current algebras. II

Stanislav PAKULIAK , Vladimir RUBTSOV and Alexey SILANTYEV

This is a continuation of the previous paper “Classical elliptic current algebras. I“ [J. Gen. Lie Theory Appl. 2 (2002), 65–78]. We describe different degenerations of the classical elliptic algebras. They yield different versions of rational and trigonometric current algebras. We also review the averaging method of Faddeev-Reshetikhin, which allows to restore elliptic algebras from the trigonometric ones.

Artigo de Pesquisa

Classical elliptic current algebras. I

Stanislav PAKULIAK , Vladimir RUBTSOV , and Alexey SILANTYEV

In this paper we discuss classical elliptic current algebras and show that there are two different choices of commutative test function algebras related to a complex torus leading to two different elliptic current algebras. Quantization of these classical current algebras gives rise to two classes of quantized dynamical quasi-Hopf current algebras studied by Enriquez, Felder and Rubtsov and by Arnaudon, Buffenoir, Ragoucy, Roche, Jimbo, Konno, Odake and Shiraishi.

Artigo de Pesquisa

Hom-algebra structures

Abdenacer MAKHLOUF and Sergei D. SILVESTROV

Hom-algebra structures are given on linear spaces by multiplications twisted by linear maps. Hom-Lie algebras and general quasi-Hom-Lie and quasi-Lie algebras were introduced by Hartwig, Larsson and Silvestrov as algebras embracing Lie algebras, super and color Lie algebras and their quasi-deformations by twisted derivations. In this paper we introduce and study Hom-associative, Hom-Leibniz and Hom-Lie admissible algebraic structures generalizing associative, Leibniz and Lie admissible algebras. Also, we characterize flexible Hom-algebras and explain some connections and differences between Hom-Lie algebras and Santilli’s isotopies of associative and Lie algebras.

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