Transposed Poisson superalgebra
| Autor: | Viktor Abramov, Olga Liivapuu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Proceedings of the Estonian Academy of Sciences, Vol 73, Iss 1, Pp 50-59 (2024) |
| Druh dokumentu: | article |
| ISSN: | 1736-6046 1736-7530 |
| DOI: | 10.3176/proc.2024.1.06 |
| Popis: | In this paper, we propose the notion of a transposed Poisson superalgebra. We prove that a transposed Poisson superalgebra can be constructed by means of a commutative associative superalgebra and an even degree derivation of this algebra. Making use of this, we construct two examples of the transposed Poisson superalgebra. One of them is the graded differential algebra of differential forms on a smooth finite dimensional manifold, where we use the Lie derivative as an even degree derivation. The second example is the commutative superalgebra of basic fields of the quantum YangâMills theory, where we use the BRST-supersymmetry as an even degree derivation to define a graded Lie bracket. We show that a transposed Poisson superalgebra has six identities that play an important role in the study of the structure of this algebra. |
| Databáze: | Directory of Open Access Journals |
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