Quantized enveloping algebras for Borcherds superalgebras

We construct quantum deformations of enveloping algebras of Borcherds superalgebras, their Verma modules, and their irreducible highest weight modules.

     

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.     

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.     

Automorphisms and primitive elements of free lie superalgebras

We consider images of primitive elements of free color Lie (p-)su per algebras under endomorphisms of these algebras Web prove that endomorphisms preserving primitivity of elements are automorphisms (Theorem 4). Note that for free groups this problem was discussed in [10], Problem 2a. At the same time we show that it is not true if we consider only images of linear combinations of elements from free generatig set (see Example, Theorem 5). We formulate some open questions. In Section 1 we give necessary definitions and collect preliminary results. In Section 2 we prove main theorems. The results of this article were presented at algebraic semi­nars of Moscow State University.     

Special Lie superalgebras with maximality condition for subalgebras

We consider finitely generated Lie superalgebras over a field of characteristic zero satisfying Capelli identities. We prove that any such an algebra with the maximality condition for abelian subalgebras is finite dimensional. In particular, any special Lie superalgebra with the maximality condition for its subalgebras has a finite dimension. We also prove that the universal enveloping algebra U(L) of special Lie superalgebra L is Noetherian if and only if $\dim L<\infty$ .     

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.     

Some generalizations of fixed point theorems and common fixed point theorems

We present some fixed point theorems and common fixed point theorems which generalize and unify previous known results.     

Fixed point subalgebras of rational higher-dimensional non-commutative tori

We consider the fixed point subalgebras of higher-dimensional rational non-commutative tori induced by finite order automorphisms derived from a diagonal extension of the canonical action on rotation algebras. We give an alternative characterization and determine their -theory.

     

Automorphisms of the lattice of all subalgebras of the semiring of polynomials in one variable

In this paper, we describe automorphisms of the lattice $ {\mathbb A} $ of all subalgebras of the semiring ?⁺[x] of polynomials in one variable over the semifield ?⁺ of nonnegative real numbers. It is proved that any automorphism of the lattice A is generated by an automorphism of the semiring ?⁺[x] that is induced by a substitution x ? px for some positive real number p. It follows that the automorphism group of the lattice $ {\mathbb A} $ is isomorphic to the group of all positive real numbers with multiplication. A technique of unigenerated subalgebras is applied.     

On fixed point and almost fixed point problems of lower semicontinuous type multivalued mappings

In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H-spaces.