Abramov, V.; Liivapuu, O. Transposed Poisson Superalgebra. Proceedings of the Estonian Academy of Sciences 2024, 73, 50, doi:10.3176/proc.2024.1.06.
Abramov, V.; Liivapuu, O. Transposed Poisson Superalgebra. Proceedings of the Estonian Academy of Sciences 2024, 73, 50, doi:10.3176/proc.2024.1.06.
Abramov, V.; Liivapuu, O. Transposed Poisson Superalgebra. Proceedings of the Estonian Academy of Sciences 2024, 73, 50, doi:10.3176/proc.2024.1.06.
Abramov, V.; Liivapuu, O. Transposed Poisson Superalgebra. Proceedings of the Estonian Academy of Sciences 2024, 73, 50, doi:10.3176/proc.2024.1.06.
Abstract
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 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 Yang-Mills theory, where we use the BRST-supersymmetry as an even degree derivation to define a graded Lie bracket. We prove several identities, which hold in a transposed Poisson superalgebra.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
