Generalized Lie algebras of type An

1998 ◽  
Vol 39 (6) ◽  
pp. 3487-3504 ◽  
Author(s):  
Volodymyr Lyubashenko ◽  
Anthony Sudbery
Keyword(s):  
Lie Algebras ◽  
Generalized Lie Algebras

Generalized Lie Algebras

1993 ◽  
pp. 247-253 ◽  
Author(s):  
U. Franz ◽  
B. Gruber
Keyword(s):  
Lie Algebras ◽  
Generalized Lie Algebras

GENERALIZED HOM-LIE STRUCTURE OF MONOIDAL HOM-ALGEBRAS IN A CATEGORY

2014 ◽  
Vol 13 (05) ◽  
pp. 1350149 ◽  
Author(s):  
LIHONG DONG ◽  
RUIFANG HUANG ◽  
SHENGXIANG WANG
Keyword(s):  
Hopf Algebra ◽  
Lie Algebras ◽  
Generalized Lie Algebras

In this paper, we study the structure of monoidal Hom-Lie algebras in the category Hℳ of H-modules for a triangular Hopf algebra (H, R) and in particular the H-Lie structure of a monoidal Hom-algebra in Hℳ by analogy with that of generalized Lie algebras.

The O'RAIFEARTAIGH Theorem for the Generalized Lie Algebras

1976 ◽  
Vol 488 (2) ◽  
pp. 93-98
Author(s):  
P. Kosiński ◽  
J. Rembieliński ◽  
P. Maślanka
Keyword(s):  
Lie Algebras ◽  
Generalized Lie Algebras

scholarly journals Engel’s Theorem for Generalized Lie Algebras

2008 ◽  
Vol 13 (1) ◽  
pp. 69-77 ◽  
Author(s):  
Mikhail Kochetov ◽  
Oana Radu
Keyword(s):  
Lie Algebras ◽  
Engel’S Theorem ◽  
Generalized Lie Algebras

The cohomology of the generalized Lie algebras

1984 ◽  
Vol 25 (8) ◽  
pp. 2550-2556 ◽  
Author(s):  
Bani Mitra ◽  
K. C. Tripathy
Keyword(s):  
Lie Algebras ◽  
Generalized Lie Algebras

Generalized Lie Algebras and Cocycle Twists

2008 ◽  
Vol 36 (11) ◽  
pp. 4032-4051 ◽  
Author(s):  
Mikhail Kochetov
Keyword(s):  
Lie Algebras ◽  
Generalized Lie Algebras

ANTI-COMMUTATIVE ALGEBRAS WITH SKEW-SYMMETRIC IDENTITIES

2009 ◽  
Vol 08 (02) ◽  
pp. 157-180 ◽  
Author(s):  
A. S. DZHUMADIL'DAEV
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Commutative Algebra ◽  
Symmetric Polynomial ◽  
Commutative Algebras ◽  
Associative Commutative Algebra ◽  
Symmetric Identities ◽  
Generalized Lie Algebras

Generalizing Lie algebras, we consider anti-commutative algebras with skew-symmetric identities of degree > 3. Given a skew-symmetric polynomial f, we call an anti-commutative algebra f-Lie if it satisfies the identity f = 0. If sn is a standard skew-symmetric polynomial of degree n, then any s4-Lie algebra is f-Lie if deg f ≥ 4. We describe a free anti-commutative super-algebra with one odd generator. We exhibit various constructions of generalized Lie algebras, for example: given any derivations D, F of an associative commutative algebra U, the algebras (U, D ∧ F) and (U, id ∧ D2) are s4-Lie. An algebra (U, id ∧ D3 - 2D ∧ D2) is s'5-Lie, where s'5 is a non-standard skew-symmetric polynomial of degree 5.

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