Related papers: The Terwilliger algebra of digraphs I -- Hamming d…

In [3], Hanaki defined the Terwilliger algebras of association schemes over a commutative unital ring. In this paper, we call the Terwilliger algebras of association schemes over a field $\mathbb{F}$ the Terwilliger $\mathbb{F}$-algebras of…

We consider endomorphism algebras of $n$-term silting complexes in derived categories of hereditary algebras, and we show that the module category of such an endomorphism algebra has a separated $n$-section. For $n=3$ we obtain a trisection…

In this paper, we explore natural connections among trigonometric Lie algebras, (general) affine Lie algebras, and vertex algebras. Among the main results, we obtain a realization of trigonometric Lie algebras as what were called the…

We classify the N = 1, 2, 3 superconformal Lie algebras of Schwimmer and Seiberg by means of differential non-abelian cohomology, and describe the general philosophy behind this new technique. The structure of the group (functor) of…

We provide an infinite family of counterexamples to the conjecture of Zassenhaus on the solvability of the outer derivation algebra of a simple modular Lie algebra. In fact, we show that the simple modular Lie algebras $H(2;(1,n))^{(2)}$ of…

Terwilliger algebras are a subalgebra of a matrix algebra constructed from an association scheme. Rie Tanaka defined what it means for a Terwilliger algebra to be almost commutative and gave five equivalent conditions. In this paper we…

Invariants of the coadjoint representation of two classes of Lie algebras are calculated. The first class consists of the nilpotent Lie algebras $T(M)$, isomorphic to the algebras of upper triangular $M\times M$ matrices. The Lie algebra…

The abelian category of tetramodules over an associative bialgebra $A$ is related with the Gerstenhaber-Schack (GS) cohomology as $Ext_\Tetra(A,A)=H_\GS(A)$. We construct a 2-fold monoidal structure on the category of tetramodules of a…

We consider a family of Hecke C*-algebras which can be realised as crossed products by semigroups of endomorphisms. We show by dilating representations of the semigroup crossed product that the category of representations of the Hecke…

Let $2.O_{m+1}$ denote the doubled Odd graph with vertex set $X$ on a set of cardinality $2m+1$, where $m\geq 1$. Fix a vertex $x_0\in X$. Let $\mathcal{A}:=\mathcal{A}(x_0)$ denote the centralizer algebra of the stabilizer of $x_0$ in the…

We consider Hecke symmetries on a 3-dimensional vector space with the associated R-symmetric algebra isomorphic to the polynomial algebra $k[x_1,x_2,x_3]$ twisted by an automorphism. The main result states that any such a Hecke symmetry is…

We introduce the concept of a triangular representation of a Lie algebra, give a counterpart of Ado's theorem, and discuss $2$-irreducible triangular modules over a nonreductive Lie algebra.

Levstein and Maldonado [F. Levstein, C. Maldonado, The Terwilliger algebra of the Johnson schemes, Discrete Mathematics 307 (2007) 1621--1635] computed the Terwilliger algebra of the Johnson scheme $J(n,m)$ when $3m\leq n$. In this paper,…

In this paper, first we introduce the notion of an embedding tensor on a 3-Lie algebra, which naturally induces a 3-Leibniz algebra. Using the derived bracket, we construct a Lie 3-algebra, whose Maurer-Cartan elements are embedding…

We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes…

We classify a class of 2-step nilpotent Lie algebras related to the representations of the Clifford algebras in the following way. Let $J\colon \Cl(\mathbb R^{r,s})\toU$ be a representation of the Clifford algebra $\Cl(\mathbb R^{r,s})$…

All solvable Lie algebras with Heisenberg nilradical have already been classified. We extend this result to a classification of solvable Leibniz algebras with Heisenberg nilradical. As an example, we show the complete classification of all…

In one of his last papers, Boris Weisfeiler proved that if modular semisimple Lie algebra possesses a solvable maximal subalgebra which defines in it a long filtration, then associated graded algebra is isomorphic to one constructed from…

Let M be a compact simply connected hyperk\"ahler (or holomorphically symplectic) manifold, \dim H^2(M)=n. Assume that M is not a product of hyperkaehler manifolds. We prove that the Lie algebra so(n-3,3) acts by automorphisms on the…

In this paper, we initiate the study of endomorphisms and modular theory of the graph C*-algebras $\O_{\theta}$of a 2-graph $\Fth$ on a single vertex. We prove that there is a semigroup isomorphism between unital endomorphisms of…