Shestakov, I.; Zhukavets, N.(Algebra and Discrete Mathematics, 2004)
We study Kuzmin’s conjecture on the index of
nilpotency for the variety N il₅ of associative nil-algebras of degree 5. Due to Vaughan-Lee [11] the problem is reduced to that
for k-generator N il₅-superalgebras, where k ...
Marini, A.; Shcherbacov, V.(Algebra and Discrete Mathematics, 2004)
In this article we study structure of autotopies,
automorphisms, autotopy groups and automorphism groups of nary linear quasigroups.
We find a connection between automorphism groups of some
special kinds of n-ary ...
Jushenko, E.(Algebra and Discrete Mathematics, 2004)
In this paper we study affine Coxeter groups. We
show how to construct decompositions of the investigated groups
into semi-direct products. We use this to give the complete list of
irreducible representations of affine ...
Mazorchuk, V.(Algebra and Discrete Mathematics, 2004)
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is
already known, present some recent estimates, and list some open
problems.
Bezushchak, O.(Algebra and Discrete Mathematics, 2004)
The inverse semigroup of partially defined co–
finite automorphisms of integers is considered. This semigroup is
presented by generators and defining relations and its growth function is described.
Kulikova, O.V.(Algebra and Discrete Mathematics, 2004)
The paper is a generalization of [2]. For a group
H = ‹A|O›, conditions for the equality Ñ₁ ∩ Ñ₂ = Ñ₁, Ñ₂] are
given in terms of pictures, where Ñi is the normal closure of a set R¯
i ⊂ H for i = 1, 2.
Krempa, J.(Algebra and Discrete Mathematics, 2004)
The uniform dimension, also known as Goldie
dimension, can be defined and used not only in the class of modules,
but also in large classes of lattices and groups. For considering this
dimension it is necessary to involve ...
Sonkin, D.(Algebra and Discrete Mathematics, 2004)
It is shown that the set of pairwise non-isomorphic
2-generated simple groups of exponent n (n ≥ 2⁴⁸ and n is odd or
divisible by 2⁹
) is of cardinality continuum. As a corollary, for any
sufficiently large n the ...
Chapovsky, Yu.A.; Kalyuzhnyi, A.A.; Podkolzin, G.B.(Algebra and Discrete Mathematics, 2004)
For the cocycle bicrossed product construction
applied to a locally compact group and its two subgroups, we give
a simple description of the group of the corresponding extensions
in terms of the second cohomology group ...
Kyrychenko, A.A.; Samoılenko, Yu.S.(Algebra and Discrete Mathematics, 2004)
Let H be a unitary (finite dimensional Hilbert) space. It is known [1] that a self-adjoint operator on H, A = A* ≥ 0, is a sum of n orthogonal projections for some n ∈ N if and only if 1) tr A ∈ N∪{0}, 2) tr A ≥ dim Im A ...
Bondarenko, V.M.(Algebra and Discrete Mathematics, 2004)
Let Λ denote an extended Dynkin diagram with
vertex set Λ0 = {0, 1,... ,n}. For a vertex i, denote by S(i) the set
of vertices j such that there is an edge joining i and j; one assumes
the diagram has a unique vertex ...
Timoshin, A.S.(Algebra and Discrete Mathematics, 2004)
In the space of irreducible unitary representations
of a linear group over an algebra of type Ā₂ an open dense subset
of representations in the general position is singled out. This set is
identified, up to simple ...
According to the canonical isomorphism between
the positive part Uq⁺(g) of the Drinfeld–Jimbo quantum group
Uq(g) and the generic composition algebra C(∆) of Λ, where the
Kac–Moody Lie algebra g and the finite ...
Andriychuk, V.(Algebra and Discrete Mathematics, 2004)
Some corollaries of the Hasse principle for Brauer
group of a pseudoglobal field are obtained. In particular we prove
Hasse-Minkowski theorem on quadratic forms over pseudoglobal
field and the Hasse principle for quadratic ...
In this article it is proved that a torsion-free
locally nilpotent groups with non-trivial Fitting subgroup and every
proper homomorphic image an N₁-group is an N₁-group(and so it
is nilpotent).
We study the class of standardly stratified algebras introduced by Cline, Parshall and Scott, and its subclass of the
so-called weakly properly stratified algebras, which generalizes the
class of properly stratified ...
Popovych, S.; Turowska, L.(Algebra and Discrete Mathematics, 2004)
The problem of unitarization of representations
of algebras generated by idempotents with linear relations is studied. Construction of non-unitarizable representations for some subintervals of continuous spectrum is ...