Vladimir Dotsenko
YOU?
Author Swipe
View article: Yamaguti algebras and noncrossing partitions
Yamaguti algebras and noncrossing partitions Open
Recently, Das defined a new type of algebras, the Yamaguti algebras, which are supposed to serve as envelopes of Lie-Yamaguti algebras appearing naturally in differential geometry. We show that the nonsymmetric operad of Yamaguti algebras …
View article: Operads of moduli spaces of points in $\mathbb{C}^d$ revisited
Operads of moduli spaces of points in $\mathbb{C}^d$ revisited Open
We study the operad structure on the homology of moduli spaces of pointed rooted trees of $d$-dimensional projective spaces, introduced by Chen, Gibney and Krashen a couple of decades ago. We describe this operad by generators and relation…
View article: Fine structures inside the pre-Lie operad revisited
Fine structures inside the pre-Lie operad revisited Open
We prove a conjecture of Chapoton from 2010 stating that the pre-Lie operad, as a Lie algebra in the symmetric monoidal category of linear species, is freely generated by the free operad on the species of cyclic Lie elements.
View article: On the conjecture of Kashuba and Mathieu about free Jordan algebras
On the conjecture of Kashuba and Mathieu about free Jordan algebras Open
Kashuba and Mathieu proposed a conjecture on vanishing of Lie algebra homology, implying a description of the $GL_d$-module structure of the free $d$-generated Jordan algebra. Their conjecture relies on a functorial version of the Tits--Ka…
View article: Volume Preservation of Butcher Series Methods from the Operad Viewpoint
Volume Preservation of Butcher Series Methods from the Operad Viewpoint Open
We study a coloured operad involving rooted trees and directed cycles of rooted trees that generalizes the operad of rooted trees of Chapoton and Livernet. We describe all the relations between the generators of a certain suboperad of that…
View article: On the conjecture of Shang about free alternative algebras
On the conjecture of Shang about free alternative algebras Open
Kashuba and Mathieu proposed a conjecture on vanishing of some components of the homology of certain Lie algebras, implying a description of the $GL_d$-module structure of the free $d$-generated Jordan algebra. Their conjecture relies on a…
View article: Global Weyl modules for thin Lie algebras are finite-dimensional
Global Weyl modules for thin Lie algebras are finite-dimensional Open
The notion of Weyl modules, both local and global, goes back to Chari and Pressley in the case of affine Lie algebras, and has been extensively studied for various Lie algebras graded by root systems. We extend that definition to a certain…
View article: DT INVARIANTS FROM VERTEX ALGEBRAS
DT INVARIANTS FROM VERTEX ALGEBRAS Open
We obtain a new interpretation of the cohomological Hall algebra $\mathcal {H}_Q$ of a symmetric quiver Q in the context of the theory of vertex algebras. Namely, we show that the graded dual of $\mathcal {H}_Q$ is naturally identified wit…
View article: Hidden structures behind ambient symmetries of the Maurer-Cartan equation
Hidden structures behind ambient symmetries of the Maurer-Cartan equation Open
For every differential graded Lie algebra $\mathfrak{g}$ one can define two different group actions on the Maurer-Cartan elements: the ubiquitous gauge action and the action of $\mathrm{Lie}_\infty$-isotopies of $\mathfrak{g}$, which we ca…
View article: Distributive lattices of varieties of Novikov algebras
Distributive lattices of varieties of Novikov algebras Open
We prove that a variety of Novikov algebras has a distributive lattice of subvarieties if and only if the lattice of its subvarieties defined by identities of degree three is distributive, thus answering, in the case of Novikov algebras, a…
View article: Reconnectads
Reconnectads Open
We introduce a new operad-like structure that we call a reconnectad; the “input” of an element of a reconnectad is a finite simple graph, rather than a finite set, and “compositions” of elements are performed according to the notion of the…
View article: A characterisation of Lie algebras using ideals and subalgebras
A characterisation of Lie algebras using ideals and subalgebras Open
We prove that if, for a non‐trivial variety of non‐associative algebras, every subalgebra of every free algebra is free and is an ideal whenever is an ideal, then this variety coincides with the variety of all Lie algebras.
View article: Chain rule symmetry for singular SPDEs
Chain rule symmetry for singular SPDEs Open
We characterise the chain rule symmetry for the geometric stochastic heat equations in the full subcritical regime for Gaussian and non-Gaussian noises. We show that the renormalised counter-terms that give a solution invariant under chang…
View article: Categorification of quiver diagonalization and Koszul algebras
Categorification of quiver diagonalization and Koszul algebras Open
In earlier work of three of the authors of the present paper, a supercommutative quadratic algebra was associated to each symmetric quiver, and a new proof of positivity of motivic Donaldson-Thomas invariants of symmetric quivers was given…
View article: Deformation theory of cohomological field theories
Deformation theory of cohomological field theories Open
We develop the deformation theory of cohomological field theories (in short, CohFTs), which is done as a special case of a general deformation theory of morphisms of modular operads. This leads us to introduce two new natural extensions of…
View article: Stable homology of Lie algebras of derivations and homotopy invariants of wheeled operads
Stable homology of Lie algebras of derivations and homotopy invariants of wheeled operads Open
We prove a theorem that computes, for any augmented operad $\mathcal{O}$, the stable homology of the Lie algebra of derivations of the free algebra $\mathcal{O}(V)$ with twisted bivariant coefficients (here stabilization occurs as $\dim(V)…
View article: Novikov algebras and multi-indices in regularity structures
Novikov algebras and multi-indices in regularity structures Open
In this work, we introduce multi-Novikov algebras, a generalisation of Novikov algebras with several binary operations indexed by a given set, and show that the multi-indices recently introduced in the context of singular stochastic partia…
View article: The three graces in the Tits--Kantor--Koecher category
The three graces in the Tits--Kantor--Koecher category Open
A metaphor of Loday describes Lie, associative, and commutative associative algebras as ``the three graces'' of the operad theory. In this article, we study the three graces in the category of $\mathfrak{sl}_2$-modules that are sums of cop…
View article: Tangent complexes and the Diamond Lemma
Tangent complexes and the Diamond Lemma Open
The celebrated Diamond Lemma of Bergman gives an effectively verifiable criterion of uniqueness of normal forms for term rewriting in associative algebras. We revisit that result in the context of deformation theory and homotopical algebra…
View article: Nilpotence, weak nilpotence, and the nil property in the nonassociative world: computations and conjectures
Nilpotence, weak nilpotence, and the nil property in the nonassociative world: computations and conjectures Open
We present some results, both rigorously mathematical and computational, showing unexpected relations between different identities expressing nilpotence in nonassociative algebras, and formulate a number of conjectural generalizations and …
View article: Identities for deformation quantizations of almost Poisson algebras
Identities for deformation quantizations of almost Poisson algebras Open
We propose an algebraic viewpoint of the problem of deformation quantization of the so called almost Poisson algebras, which are algebras with a commutative associative product and an antisymmetric bracket which is a bi-derivation but does…
View article: Fine structures inside the PreLie operad revisited
Fine structures inside the PreLie operad revisited Open
We prove a conjecture of Chapoton from 2010 stating that the pre-Lie operad, as a Lie algebra in the symmetric monoidal category of linear species, is freely generated by the free operad on the species of cyclic Lie elements.
View article: Generalized Cohomological Field Theories in the Higher Order Formalism
Generalized Cohomological Field Theories in the Higher Order Formalism Open
In the classical Batalin—Vilkovisky formalism, the BV operator is a differential operator of order two with respect to a commutative product; in the differential graded setting, it is known that if the BV operator is homotopically trivial,…
View article: Maurer-Cartan methods in deformation theory: the twisting procedure
Maurer-Cartan methods in deformation theory: the twisting procedure Open
This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment of the twisting procedure, which functorially creates new di…
View article: Reconnectads
Reconnectads Open
We introduce a new operad-like structure that we call a reconnectad; the ``input'' of an element of a reconnectad is a finite simple graph, rather than a finite set, and ``compositions'' of elements are performed according to the notion of…
View article: A characterisation of Lie algebras using ideals and subalgebras
A characterisation of Lie algebras using ideals and subalgebras Open
We prove that if, for a nontrivial variety of non-associative algebras, every subalgebra of every free algebra is free and $I^2$ is an ideal whenever $I$ is an ideal, then this variety coincides with the variety of all Lie algebras.
View article: Polynomial identities in Novikov algebras
Polynomial identities in Novikov algebras Open
In this paper, we study Novikov algebras satisfying nontrivial identities. We show that a Novikov algebra over a field of zero characteristic that satisfies a nontrivial identity satisfies some unexpected "universal" identities, in particu…