相关论文: Two vertex geometrically irreducible algebras
We construct infinitely many manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings. Both closed manifolds and manifolds with boundary tori are constructed.
There exists two types of nonassociative algebras whose associator satisfies a symmetric relation associated with a 1-dimensional invariant vector space with respect to the natural action of the symmetric group on three elements. The first…
In this work we study Leibniz algebras whose second-maximal subalgebras are ideals. We provide a classification based on solvability, nilpotency, and the size of the derived algebra. We give specific descriptions of those Leibniz algebras…
We classify non-reductive four-dimensional homogeneous conformally Einstein manifolds.
We construct a new family of infinite-dimensional quasi-graded Lie algebras on hyperelliptic curves. We show that constructed algebras possess infinite number of invariant functions and admit a decomposition into the direct sum of two…
We give a geometric classification of all $6$-dimensional nilpotent Tortkara algebras over $\mathbb C$
Hom-algebras are generalizations of algebras obtained using a twisting by a linear map. But there is a priori a freedom on where to twist. We enumerate here all the possible choices in the Lie and associative categories and study the…
We describe differential invariants of infinite-dimensional algebras being equivalence algebras of some classes of PDE and study structure of these algebras.
We are continuing our study of ADE-orbifold subalgebras of the triplet vertex algebra W(p). This part deals with the dihedral series. First, subject to a certain constant term identity, we classify all irreducible modules for the vertex…
For an infinite chain bicomplex we show that the orthogonality and grading conditions provide it with the structure of a bigraded differential algebra with respect to a natural multiplication of several elements bicomplex spaces.…
We obtain a description of the irreducible representation algebra of the alternating group of degree four over the ring of 2-adic integers.
We first recall two equivalent definitions of Lie $2$-algebras, categorification of Lie algebras and $2$-term $L_\infty$-algebras. Then we present four different kinds of Lie $2$-algebras from $2$-plectic manifolds, Courant algebroids,…
Let $V$ be a vertex operator algebra and $g$ an automorphism of finite order. We construct an associative algebra $A_g(V)$ and a pair of functors between the category of $A_g(V)$-modules and a certain category of admissible $g$-twisted…
We show that for a gradable finite dimensional algebra the perfect complexes and bounded derived category cannot be distinguished by homotopy invariants.
Hom-quadri dendriform algebras and Hom-six-dendriform agebras are introduced and studied which is a splitting of a Hom-diassociative and Hom-triassociative algebras, respectively. Moreover we explore the connections be tween these…
The notions of vertex Lie algebra and vertex Poisson algebra are presented and connections among vertex Lie algebras, vertex Poisson algebras and vertex algebras are discussed.
We classify (possibly non commutative) algebras of low rank over a domain R. We first review results for algebras of rank 2 and for finite-dimensional division algebras over the real numbers. These results motivate us to consider which…
A commutative associative algebra $A$ over ${\mathbb C}$ with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for $A$ as a vertex algebra and the modules for $A$ as an…
We give a complete classification (up to isomorphism) of Lie conformal algebras which are free of rank two as $\C[\partial]$-modules, and determine their automorphism groups.
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…