scholarly journals Tensor Representations of Classical Locally Finite Lie Algebras

Author(s):  
Ivan Penkov ◽  
Konstantin Styrkas
1971 ◽  
Vol s2-3 (2) ◽  
pp. 334-340 ◽  
Author(s):  
I. N. Stewart
Keyword(s):  

2019 ◽  
Vol 19 (08) ◽  
pp. 2050149
Author(s):  
Shanshan Liu ◽  
Lina Song ◽  
Rong Tang

In this paper, first we study dual representations and tensor representations of Hom-pre-Lie algebras. Then we develop the cohomology theory of regular Hom-pre-Lie algebras in terms of the cohomology theory of regular Hom-Lie algebras. As applications, we study linear deformations of regular Hom-pre-Lie algebras, which are characterized by the second cohomology groups of regular Hom-pre-Lie algebras with the coefficients in the regular representations. The notion of a Nijenhuis operator on a regular Hom-pre-Lie algebra is introduced which can generate a trivial linear deformation of a regular Hom-pre-Lie algebra. Finally, we introduce the notion of a Hessian structure on a regular Hom-pre-Lie algebra, which is a symmetric nondegenerate 2-cocycle with the coefficient in the trivial representation. We also introduce the notion of an [Formula: see text]-operator on a regular Hom-pre-Lie algebra, by which we give an equivalent characterization of a Hessian structure.


2004 ◽  
Vol 32 (12) ◽  
pp. 4613-4631 ◽  
Author(s):  
Guang'ai Song ◽  
Yucai Su
Keyword(s):  

1998 ◽  
Vol 77 (2) ◽  
pp. 362-386 ◽  
Author(s):  
AA Baranov
Keyword(s):  

2003 ◽  
Vol 80 (5) ◽  
pp. 478-485 ◽  
Author(s):  
Ivan Penkov ◽  
Helmut Strade

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