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BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
Інший ID:
2010 Mathematics Subject Classification: 17A99; 18D10; 16T99
DOI:10.3842/SIGMA.2015.086
DOI:10.3842/SIGMA.2015.086
Посилання:
BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras / G. Graziani, A. Makhlouf, C. Menini, F. Panaite // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 32 назв. — англ.
Підтримка:
This paper was written while Claudia Menini was a member of GNSAGA. Florin Panaite was
supported by a grant of the Romanian National Authority for Scientific Research, CNCSUEFISCDI,
project number PN-II-ID-PCE-2011-3-0635, contract nr. 253/5.10.2011. Parts of
this paper have been written while Florin Panaite was a visiting professor at University of Ferrara
in September 2014, supported by INdAM, and a visiting scholar at the Erwin Schrodinger
Institute in Vienna in July 2014 in the framework of the “Combinatorics, Geometry and Physics”
programme; he would like to thank both these institutions for their warm hospitality.
The authors are grateful to the referees for their remarks and questions.
Дата:
2015
Переглядів:
619
Завантажень:
265
Анотація:
A BiHom-associative algebra is a (nonassociative) algebra A endowed with two commuting multiplicative linear maps α,β:A→A such that α(a)(bc)=(ab)β(c), for all a,b,c∈A. This concept arose in the study of algebras in so-called group Hom-categories. In this paper, we introduce as well BiHom-Lie algebras (also by using the categorical approach) and BiHom-bialgebras. We discuss these new structures by presenting some basic properties and constructions (representations, twisted tensor products, smash products etc).
