Polynomial identities in Novikov algebras

Dotsenko, Vladimir; Ismailov, Nurlan; Umirbaev, Ualbai

doi:10.1007/s00209-023-03231-8

Cited by 8 publications

(4 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 An analog of the present theorem was proven in [13]. Namely, the authors proved that if a unital transposed Poisson algebra satisfies a [•, •]-free polynomial identity (depending only on the multiplication •), then this algebra satisfies an identity of the type…”

Section: Transposed Poisson Pi Algebrasmentioning

confidence: 79%

Transposed Poisson Structures

Damas Beites,

Ferreira,

Kaygorodov

2024

Results Math

View full text Add to dashboard Cite

show abstract

Section: Transposed Poisson Pi Algebrasmentioning

confidence: 79%

Transposed Poisson Structures

Damas Beites,

Ferreira,

Kaygorodov

2024

Results Math

View full text Add to dashboard Cite

show abstract

“…Let us remark that there is one interesting question about universal multiplicative enveloping algebras of pre-Lie algebras that still awaits a clear answer. It follows from the results of the first author and Umirbaev [ 13 ] that for a free pre-Lie algebra L , the associative algebra is free. In the language of species, the twisted associative algebra is free, and one may wish to describe its species of generators.…”

Section: Universal Multiplicative Envelopes and Kähler Differentialsmentioning

confidence: 99%

“…The authors thank Anton Khoroshkin, Martin Markl and Pedro Tamaroff for several useful comments, and the anonymous referee for very careful reading of the paper. Special thanks are due to Frederic Chapoton whose remarks on [ 13 ] made us discover Theorem 3. This work was supported by Institut Universitaire de France, by Fellowship USIAS-2021-061 of the University of Strasbourg Institute for Advanced Study through the French national program “Investment for the future” (IdEx–Unistra), and by the French national research agency (project ANR-20-CE40-0016).…”

Section: Acknowledgementsmentioning

confidence: 99%

Three Schur functors related to pre-Lie algebras

DOTSENKO,

FLYNN-CONNOLLY

2023

Math. Proc. Camb. Phil. Soc.

View full text Add to dashboard Cite

We give explicit combinatorial descriptions of three Schur functors arising in the theory of pre-Lie algebras. The first of them leads to a functorial description of the underlying vector space of the universal enveloping pre-Lie algebra of a given Lie algebra, strengthening the Poincaré-Birkhoff-Witt (PBW) theorem of Segal. The two other Schur functors provide functorial descriptions of the underlying vector spaces of the universal multiplicative enveloping algebra and of the module of Kähler differentials of a given pre-Lie algebra. An important consequence of such descriptions is an interpretation of the cohomology of a pre-Lie algebra with coefficients in a module as a derived functor for the category of modules over the universal multiplicative enveloping algebra.

show abstract

“…Which algebraic condition may replace the associativity in the quantization of almost Poisson structures which are not Lie-Poisson? The possibilities of imposing identities in the deformed algebra have been considerably reduced by the no-go results [17][18][19] and practically closed by the recent work [20]. A promising algebraic framework seems to be provided by the strong homotopy associative algebras A ∞ [21,22].…”

Section: Introductionmentioning

confidence: 99%