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On the Special Identities of Gelfand–Dorfman Algebras
Experimental Mathematics. 2022. Vol. 33. No. 1. P. 165–174.
Колесников П. С.
Колесников П. С., Algebras and Representation Theory 2021 Vol. 25 No. 4 P. 847–867
Added: March 5, 2024
Колесников П. С., European Journal of Mathematics 2023 Vol. 9 No. 2 P. 1–18
Added: March 5, 2024
Ignatyev Mikhail, Petukhov A., Journal of Algebra 2021 Vol. 585 P. 501–557
Let $\mathfrak{n}$ be a locally nilpotent infinite-dimensional Lie algebra over $\mathbb{C}$. Let $\mathrm{U}(\mathfrak{n})$ and $\mathrm{S}(\mathfrak{n})$ be its respective universal enveloping algebra and symmetric algebra. Consider the Jacobson topology on the primitive spectrum of $\mathrm{U}(\mathfrak{n})$, and the Poisson topology on the primitive Poisson spectrum of $\mathrm{S}(\mathfrak{n})$.
We provide a homeomorphism between the corresponding topological spaces (at the ...
Added: October 8, 2023
Lopatkin V., / Series arXiv "math". 2021.
This paper shows how to obtain the key concepts and notations of Garside theory by using the Composition--Diamond lemma. We also show in some cases the greedy normal form is exactly a Gröbner--Shirshov normal form and a family of a left-cancellative category is a Garside family, if and only if a suitable set of reductions ...
Added: October 29, 2021
Lopatkin V., Nam T. G., Journal of Algebra 2017 No. 481 P. 273–292
In this paper, we give sharp bounds for the homological dimensions of the Leavitt path algebra LK(E) of a finite graph E with coefficients in a commutative ring K, as well as establish a formula for calculating the homological dimensions of LK(E) when K is a commutative unital algebra over a field. ...
Added: October 29, 2021
Cherkasov A., Piontkovski D., , in: ISSAC '21: Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation.: Association for Computing Machinery (ACM), 2021. P. 91–98.
Two operads are said to belong to the same Wilf class if they have the same generating series. We discuss possible Wilf classifications of non-symmetric operads with monomial relations. As a corollary, this would give the same classification for the operads with a finite Groebner basis.
Generally, there is no algorithm to decide whether two finitely ...
Added: September 27, 2021
Bokut L., Chen Y., Kalorkoti K. et al., World Scientific Publishing Co. Pte. Ltd, 2020.
The book is about (associative, Lie and other) algebras, groups, semigroups presented by generators and defining relations. They play a great role in modern mathematics. It is enough to mention the quantum groups and Hopf algebra theory, the Kac–Moody and Borcherds algebra theory, the braid groups and Hecke algebra theory, the Coxeter groups and semisimple ...
Added: September 27, 2021
Markaryan N. S., Forum Mathematicum 2021 Vol. 33 No. 2 P. 531–545
We apply Weyl n-algebras to prove formality theorems for higher Hochschild cohomology. We
present two approaches: via propagators and via the factorization complex. It is shown that the second
approach is equivalent to the first one taken with a new family of propagators we introduce. ...
Added: March 15, 2021
Markaryan N. S., / Series arXiv "math". 2020.
We apply Weyl n-algebras to prove formality theorems for higher Hochschild cohomology. We present two approaches: via propagators and via the factorization complex. It is shown that the second approach is equivalent to the first one taken with a new family of propagators we introduce. ...
Added: October 16, 2020
Piontkovski D., , in: ISSAC '17 International Symposium on Symbolic and Algebraic Computation. Kaiserslautern, Germany — July 25 - 28, 2017. ACM, New York, 454 pp.: NY: ACM, 2017. P. 373–380.
We consider varieties of linear multioperator algebras, that is, classes of algebras with several multilinear operations satisfying certain identities. To each such a variety one can assign a numerical sequence called a sequence of codimensions. The n-th codimension is equal to the dimension of the vector space of all n-linear operations in the free algebra ...
Added: September 15, 2017
Soukhanov L., / Series math "arxiv.org". 2015.
We study the enumerative geometry of orbits of multidimensional toric action on projective algebraic varieties and develop a new cyclic differential-graded operad, conjecturally governing the real version of the enumerative geometry of these toric orbits. ...
Added: November 18, 2015
Piontkovski D., Khoroshkin A., Journal of Algebra 2014 P. 1–53
For an operad P with a finite Gröbner basis of relations, we study the generating functions for the dimensions of its graded components P(n). Under moderate assumptions on the relations we prove that the exponential generating function for the sequence {dimP(n)} is differential algebraic, and in fact algebraic if P is a symmetrization of a ...
Added: March 5, 2015
Khoroshkin A., Piontkovski D., Journal of Algebra 2015 Vol. 426 P. 377–429
Given an operad P with a finite Gröbner basis of relations, we study the generating functions for the dimensions of its graded components P(n). Under moderate assumptions on the relations we prove that the exponential generating function for the sequence {dimP(n)} is differential algebraic, and in fact algebraic if P is a symmetrization of a ...
Added: February 2, 2015
Khoroshkin A., Piontkovski D., / Series math "arxiv.org". 2014. No. arXiv:1202.5170.
Given an operad P with a finite Grobner basis of relations, we study the generating functions for the dimensions of its graded components P(n). Under moderate assumptions on the relations we prove that the exponential generating function for the sequence {dim P(n)} is differential algebraic, and in fact algebraic for P is a symmetrization of ...
Added: May 13, 2014
Khoroshkin, A., Markarian, N., Shadrin, S., Communications in Mathematical Physics 2013 Vol. 322 No. 3 P. 697–729
We give an explicit formula for a quasi-isomorphism between the operads Hycomm (the homology of the moduli space of stable genus 0 curves) and BV/Δ (the homotopy quotient of Batalin-Vilkovisky operad by the BV-operator). In other words we derive an equivalence of Hycomm-algebras and BV-algebras enhanced with a homotopy that trivializes the BV-operator. These formulas ...
Added: August 23, 2013