The Cohomology Structure of Hom-H-Pseudoalgebras
The goal of this paper is to study cohomological theory of Hom-associative H-pseudoalgebras and Hom–Lie H-pseudoalgebras. We define Gerstenhaber bracket on the space of multilinear mappings of Hom-associative H-pseudoalgebra. Furthermore, the symmetric Schouten product and alternating Schouten product are studied. Using the Gerstenhaber bracket and alternating Schouten product, differential graded Lie algebra are constructed on the space of multilinear mappings of Hom-associative H-pseudoalgebra and Hom-Lie H-pseudoalgebras.
KeywordsHom-associative-H-pseudoalgebra Hom–Lie H-pseudoalgebra Gerstenhaber bracket Schouten product Cohomology
Mathematics Subject Classification17A30 17B20 17B81
Qinxiu Sun has been partially supported by the National Natural Science Foundation of China (No. 11401530 and 11226069 ) and the Natural Science Foundation of Zhejiang Province of China (No. Y19A010005 and LQ13A010018).
- Ammar,F., Ejbehi,Z., Makhlouf, A.: Cohomology and deformations of Hom-algebras, arXiv:1005.0456v1, 2010
- Kac,V.G.: The idea of locality, Physical applications and mathematical aspects of geometry, groups and algebras. In: H.-D. Doebner et al, (ed.) pp. 16-32, World Sci., Singapore (1997), arXiv:q-alg/9709008v1
- Kac,V.G. : Formal distribution algebras and conformal algebras. In: XII-th international congress in mathematical physics (ICMP’97) (Brisbane), Internat. Press: Cambridge, MA, pp. 80-97 (1999)Google Scholar
- Lecomte,P., Schicketanz,H.: The multigraded Nijenhuis-Richardson algebra, its universal property and applications, arxiv: math/920T257 (1992)
- Sweedler, M.: Hopf algebras, Math. lecture notes series. Benjamin, New York (1969)Google Scholar