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Let $L$ be a Lie algebra of Block type over $C$ with basis ${L_{alpha,i},|,alpha,iinZ}$ and brackets $[L_{alpha,i},L_{beta,j}]=(beta(i+1)-alpha(j+1))L_{alpha+beta,i+j}$. In this paper, we shall construct a formal distribution Lie algebra of $L$. Then we decide its conformal algebra $B$ with $C[partial]$-basis ${L_alpha(w),|,alphainZ}$ and $lambda$-brackets $[L_alpha(w)_lambda L_beta(w)]=(alphapartial+(alpha+beta)lambda)L_{alpha+beta}(w)$. Finally, we give a classification of free intermediate series $B$-modules.
Let $A$ be a split finite-dimensional associative unital algebra over a field. The first main result of this note shows that if the Ext-quiver of $A$ is a simple directed graph, then $HH^1(A)$ is a solvable Lie algebra. The second main result shows t
In this paper, we introduce a class of infinite Lie conformal algebras $mathfrak{B}(alpha,beta,p)$, which are the semi-direct sums of Block type Lie conformal algebra $mathfrak{B}(p)$ and its non-trivial conformal modules of $Z$-graded free intermedi
We show that if $B$ is a block of a finite group algebra $kG$ over an algebraically closed field $k$ of prime characteristic $p$ such that $HH^1(B)$ is a simple Lie algebra and such that $B$ has a unique isomorphism class of simple modules, then $B$
In this paper we describe some Leibniz algebras whose corresponding Lie algebra is four-dimensional Diamond Lie algebra $mathfrak{D}$ and the ideal generated by the squares of elements (further denoted by $I$) is a right $mathfrak{D}$-module. Using d
In the present paper we describe Leibniz algebras with three-dimensional Euclidean Lie algebra $mathfrak{e}(2)$ as its liezation. Moreover, it is assumed that the ideal generated by the squares of elements of an algebra (denoted by $I$) as a right $m