Witt型李超代数的极大根阶化子代数

设W(m,n)是特征p3的代数闭域上有限维Witt型李超代数.证明了W(m,n)的极大根阶化子代数一定是其极大Z-阶化子代数,从而刻画了W(m,n)的所有极大根阶化子代数.结果有助于理解Witt型李超代数W(m,n)的内在性质.     

The abelian subalgebras of maximal dimensions for general linear Lie superalgebras

Over an algebraically closed field of characteristic zero, all the abelian subalgebras of maximal dimensions for the general linear Lie superalgebras are classified in the sense of conjugation. As a consequence, the minimal faithful representations are determined for the so-called nice abelian Lie superalgebras.     

Special odd Lie superalgebras in prime characteristic

Let g be a finite dimensional special odd Lie superalgebra over an algebraically closed field F of characteristic p > 3.The sufficient and necessary condition is given for g possessing a nondegenerate associative form and in this case the second cohomology group H 2 (g,F) is completely determined.     

Maximal subalgebras of Jordan superalgebras

The maximal subalgebras of the finite-dimensional simple special Jordan superalgebras over an algebraically closed field of characteristic 0 are studied. This is a continuation of a previous paper by the same authors about maximal subalgebras of simple associative superalgebras, which is instrumental here.     

Lie superalgebras

Results pertaining to the theory of representations of classical Lie superalgebras are collected in the survey.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 25, pp. 3–50, 1984.     

Detecting cohomology for Lie superalgebras

In this paper we use invariant theory to develop the notion of cohomological detection for Type I classical Lie superalgebras. In particular we show that the cohomology with coefficients in an arbitrary module can be detected on smaller subalgebras. These results are used later to affirmatively answer questions, which were originally posed in Boe et al. (2010) [5] and Bagci et al. (2008) [2], about realizing support varieties for Lie superalgebras via rank varieties constructed for the smaller detecting subalgebras.     

Groups with weak maximality condition for nonnilpotent subgroups

A group G satisfies the weak maximality condition for nonnilpotent subgroups [or, briefly, the Wmax-(nonnil) condition if G does not have infinite increasing chains {H _n | n ∈ ℕ} of nonnilpotent subgroups such that the indices |H _n+1: H _n | are infinite for each n ∈ ℕ. We study the structure of hypercentral groups satisfying the weak maximality condition for nonnilpotent subgroups. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1068–1083, August, 2006.     

Borel-Weil-Bott theory for classical Lie superalgebras

The paper is devoted to a systematic construction of the elements of Borel-Weil-Bott theory in the supercase. The main result is a presentation of the cohomology of typical irreducible G-sheaves on G/B, where G is the connected component of the identity in a classical complex Lie supergroup and B G an arbitrary Borel subsupergroup. Also presented are some simple known results concerning the cohomology of irreducible G-sheaves on G/P for a parabolic subsupergroup P.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 32, pp. 71–124, 1988.     

Lie superderivations of superalgebras

The aim of this paper is to investigate Lie superderivations of superalgebras, using the theory of functional identities in superalgebras. As a consequence, we obtain a definitive result on Lie superderivations of prime superalgebras.     

Super-biderivations of Lie superalgebras

In this paper, we attempt to investigate the super-biderivations of Lie superalgebras. Furthermore, we prove that all super-biderivations on the centerless super-Virasoro algebras are inner super-biderivations. Finally, we study the linear super commuting maps on the centerless super-Virasoro algebras.     

Identities for Lie superalgebras with a nilpotent commutator subalgebra

It is proved that the exponential growth rate of identities in any superalgebra with a nilpotent commutator subalgebra over a field of zero characteristic is an integer. Supported by RFBR (project Nos. 07-01-00080 and 06-01-00485) and by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-1983.2008.1). Translated from Algebra i Logika, Vol. 47, No. 5, pp. 617–645, September–October, 2008.     

Groups with a maximality condition for some non-normal subgroups

We describe (generalized) soluble-by-finite groups in which the set of non-normal subgroups which are not finitely generated satisfies the maximal condition.     

Infinite-dimensional Hamiltonian Lie superalgebras

The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements. We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.     

Pi-envelopes of Lie superalgebras

In this paper we find necessary and sufficient conditions on a finite-dimensional Lie superalgebra under which any associative PI-envelope of is finite-dimensional. We also extend M. Scheunert's result which enables one to pass from color Lie superalgebras to the ordinary ones, to the case of gradings by an arbitrary abelian group.