Algebra and Discrete Mathematics. - № 1 (23). - 2017
http://hdl.handle.net/123456789/4603
2021-02-25T08:34:52ZA new way to construct 1-singular Gelfand-Tsetlin modules
http://hdl.handle.net/123456789/4624
A new way to construct 1-singular Gelfand-Tsetlin modules
Zadunaisky, P.
We present a simplified way to construct the
Gelfand-Tsetlin modules over gl(n, C) related to a 1-singular GT-
tableau defined in [6]. We begin by reframing the classical construc-
tion of generic Gelfand-Tsetlin modules found in [3], showing that
they form a flat family over generic points of C(
n
2)
. We then show
that this family can be extended to a flat family over a variety
including generic points and 1-singular points for a fixed singular
pair of entries. The 1-singular modules are precisely the fibers over
these points.
Zadunaisky P. A new way to construct 1-singular Gelfand-Tsetlin modules / P. Zadunaisky // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 1. - Рp. 180-193
2017-01-01T00:00:00ZEquivalence of Carter diagrams
http://hdl.handle.net/123456789/4623
Equivalence of Carter diagrams
Stekolshchik, R.
We introduce the equivalence relation ρ on the
set of Carter diagrams and construct an explicit transformation of
any Carter diagram containing l-cycles with l > 4 to an equivalent
Carter diagram containing only 4-cycles. Transforming one Carter
diagram Γ1 to another Carter diagram Γ2 we can get a certain
intermediate diagram Γ′ which is not necessarily a Carter diagram.
Such an intermediate diagram is called a connection diagram. The
relation ρ is the equivalence relation on the set of Carter diagrams
and connection diagrams. The properties of connection and Carter
diagrams are studied in this paper. The paper contains an alternative
proof of Carter’s classification of admissible diagrams.
Stekolshchik R. Equivalence of Carter diagrams / R.Stekolshchik // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 1. - Рp.138-179
2017-01-01T00:00:00ZDg algebras with enough idempotents, their dg modules and their derived categories
http://hdl.handle.net/123456789/4622
Dg algebras with enough idempotents, their dg modules and their derived categories
M., Saorín
We develop the theory dg algebras with enough
idempotents and their dg modules and show their equivalence with
that of small dg categories and their dg modules. We introduce the
concept of dg adjunction and show that the classical covariant tensor-
Hom and contravariant Hom-Hom adjunctions of modules over
associative unital algebras are extended as dg adjunctions between
categories of dg bimodules. The corresponding adjunctions of the
associated triangulated functors are studied, and we investigate
when they are one-sided parts of bifunctors which are triangulated
on both variables. We finally show that, for a dg algebra with enough
idempotents, the perfect left and right derived categories are dual
to each other.
Saorín M. Dg algebras with enough idempotents, their dg modules and their derived categories / M. Saorín // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 1. - Рp.62-137
2017-01-01T00:00:00ZOn the representation type of Jordan basic algebras
http://hdl.handle.net/123456789/4621
On the representation type of Jordan basic algebras
Kashuba, I.; Ovsienko, S.; Shestakov, I.
A finite dimensional Jordan algebra J over a field k is called basic if the quotient algebra J/ Rad J is isomorphic to a direct sum of copies of k. We describe all basic Jordan algebras J with (Rad J) 2 = 0 of finite and tame representation type over an algebraically closed field of characteristic 0.
Kashuba I. On the representation type of Jordan basic algebras / I.Kashuba, S.Ovsienko, I.Shestakov // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 1. - Рp. 47-61
2017-01-01T00:00:00Z