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Let β be a Lie algebra of Block type with basis {Lɑ, i | ɑ ... Z, i ... Z+} and relations [Lɑ, i, Lβ, j] = (ɑ -- 1)(j + 1) -- (β -- l)(i + l))Lɑ+β,i+j. In the present paper, the derivation algebra and automorphism group of B are explicitly described. In particular, it is shown that the outer derivation space is 1-dimensional and the inner automorphism group of β is trivial. [ABSTRACT FROM AUTHOR]

In this paper, Lie bialgebra structures on the extended Schrödinger-Virasoro Lie algebra $\mathcal{L}$ are classified. It is obtained that all the Lie bialgebra structures on $\mathcal{L}$ are triangular coboundary. As a by-product, it is derived that the first cohomology group $H^1(\mathcal{L},\mathcal{L}\otimes\mathcal{L})$ is trivial. [ABSTRACT FROM AUTHOR]

Let G be a finite group and p a prime. We say that G is quasisupersoluble (resp., p-quasisupersoluble) if for every non-cyclic chief factor H/K of G (resp., for every non-cyclic chief factor H/K of G of order divisible by p), every automorphism of H/K induced by an element of G is inner. In this paper, we study the structure of quasisupersoluble and p-quasisupersoluble finite groups. [ABSTRACT FROM AUTHOR]

Let G be a non-abelian group. The non-commuting graph $\mathcal{A}_G$ of G is defined as the graph whose vertex set is the non-central elements of G and two vertices are joint if and only if they do not commute. In a finite simple graph Γ, the maximum size of complete subgraphs of Γ is called the clique number of Γ and denoted by ω(Γ). In this paper, we characterize all non-solvable groups G with $\omega(\mathcal{A}_G)\leq 57$, where 57 is the clique number of the non-commuting graph of the projective special linear group PSL(2,7). We also determine $\omega(\mathcal{A}_G)$ for all finite minimal simple groups G. [ABSTRACT FROM AUTHOR]

Point algebras introduced by Evans are algebraic systems which capture the essence of multiplications (a,b) · (c,d)=(p,q) defined on the set of all ordered pairs of elements of a set S, where p and q are selected from among a,b,c,d by some well-defined rule. In 1961, Jonsson and Tarski gave an interesting example of a variety of algebras of type 〈2,1,1〉 for illustrating the failure of certain free algebra properties. In this paper, we show that this equational class of algebras, called the JT-variety, is a universal variety of point algebras in the sense that every variety generated by a point algebra is a reduct of the JT-variety. [ABSTRACT FROM AUTHOR]

In this paper, we study the class $\widetilde{\mathcal{FI}}$ of complexes of FP-injective left R-modules. It is shown that the pair $(^{\bot}\widetilde{\mathcal{FI}},\widetilde{\mathcal{FI}})$ is a complete cotorsion pair. If R is a left coherent ring, it is proved that every complex has an $\widetilde{\mathcal{FI}}$-cover. We also introduce the FP-injective dimension of complexes. A special attention is paid to the dimension of homologically bounded above R-complexes over a left coherent ring which has a nice functorial description. [ABSTRACT FROM AUTHOR]

Let H be a weak Hopf algebra. In this paper, it is proved that the monoidal category $^H_H{\cal M}^H_H$ of weak Hopf bimodules studied in Wang [19] is equivalent to the monoidal category ${\cal YD}^H_H$ of weak Yetter-Drinfel'd modules introduced in Böhm [2]. When H has a bijective antipode, a braiding in the category $^H_H{\cal M}^H_H$ is constructed by the braiding on ${\cal YD}^H_H$, generalizing the main result in Schauenburg [14]. Finally, the braided Lie structures of an algebra A in the category $_H^H{\cal M}^H_H$ are investigated, by showing that if A is a sum of two braided commutative subalgebras, then the braided commutator ideal of A is nilpotent. [ABSTRACT FROM AUTHOR]