Algebras and Representation Theory
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Minuscule Schubert Varieties: Poset Polytopes, PBW-Degenerated Demazure Modules, and Kogan Faces
Algebras and Representation Theory - Tập 18 - Trang 1481-1503 - 2015
We study a family of posets and the associated chain and order polytopes. We identify the order polytope as a maximal Kogan face in a Gelfand-Tsetlin polytope of a multiple of a fundamental weight. We show that the character of such a Kogan face equals to the character of a Demazure module which occurs in the irreducible representation of
......
Comparing Invariants of SK1
Algebras and Representation Theory - Tập 16 - Trang 729-745 - 2011
In this text, we compare an invariant of the reduced Whitehead group SK
1 of a central simple algebra recently introduced by Kahn (2010) to other invariants of SK
1. Doing so, we prove the non-triviality of Kahn’s invariant using the non-triviality of an invariant introduced by Suslin (1991) which is non-trivial for Platonov’s examples of non-trivial SK
......
Finitistic Extension Degree
Algebras and Representation Theory - Tập 17 - Trang 495-506 - 2013
We introduce the finitistic extension degree of a ring and investigate rings for which it is finite. The Auslander–Reiten Conjecture is proved for rings of finite finitistic extension degree and these rings are also shown to have finite finitistic dimension. We apply these results to better understand a generalized version of the Auslander–Reiten Condition for Gorenstein rings. We also record how ......
Verifying Huppert’s Conjecture for PSp4(q) when q > 7
Algebras and Representation Theory - Tập 15 - Trang 427-448 - 2010
Let G denote a finite group and cd (G) the set of irreducible character degrees of G. Bertram Huppert conjectured that if H is a finite nonabelian simple group such that cd (G) = cd (H), then G ≅ H × A, where A is an abelian group. Huppert verified the conjecture for PSp4(q) when q = 3, 4, 5, or 7. In this paper, we extend Huppert’s results and verify the conjecture for PSp4(q) for all q. This dem......
On Quantized Decomposition Maps for Graded Algebras
Algebras and Representation Theory - Tập 19 - Trang 135-146 - 2015
Decomposition maps control the representation theory of algebras obtained through the process of specialization. In this note, we study a factorization result for graded decomposition maps associated with the specializations of graded algebras. We obtain results previously known only in the ungraded setting.
Sign-Coherence of C-Vectors and Maximal Green Sequences for Acyclic Sign-Skew-Symmetric Matrices
Algebras and Representation Theory - Tập 24 - Trang 811-827 - 2020
In this paper we construct an unfolding for c −vectors of acyclic sign-skew symmetric matrices and we also prove that the sign-coherence property holds for acyclic sign-skew-symmetric matrices. Then we prove that every acyclic sign-skew-symmetric matrix admits a maximal green sequence.
k-Modules Over Linear Spaces by n-Linear Maps Admitting a Multiplicative Basis
Algebras and Representation Theory - Tập 22 - Trang 615-626 - 2018
We study the structure of certain k-modules 𝕍 over linear spaces 𝕎 with restrictions neither on the dimensions of 𝕍 and 𝕎 nor on the base field 𝔽. A basis
$\mathfrak {B} = \{v_{i}\}_{i\in I}$
of 𝕍 is called multiplicative with respect to th......
Graded Identities and Central Polynomials for the Verbally Prime Algebras
Algebras and Representation Theory - Tập 26 - Trang 71-96 - 2021
Let F be a field of characteristic zero and let R be an algebra that admits a regular grading by an abelian group H. Moreover, we consider G a group and let A be an algebra with a grading by the group G × H, we define the R-hull of A as the G × H-graded algebra given by
$\mathfrak {R}(A)=\oplus _{(g,h)\in G\time......
On a Family of Representations of Residually Finite Groups
Algebras and Representation Theory - Tập 23 - Trang 1727-1735 - 2019
For a residually finite group G, its normal subgroups G ⊃ G1 ⊃ G2⋯ with
$\cap _{n\in \mathbb N}G_{n}=\{e\}$
and for a growth function γ we construct a unitary representation πγ of G. For the minimal growth, πγ is weakly equivalent to the regular representation, and for the maximal growth it is weakly equivalent to the direct sum of the quasiregular representations on the quotients G/Gn. In the ......
A Locally Trivial Quantum Hopf Fibration
Algebras and Representation Theory - Tập 9 - Trang 121-146 - 2006
The irreducible *-representations of the polynomial algebra
$\mathcal{O}(S^{3}_{pq})$
of the quantum3-sphere introduced by Calow and Matthes are classified. The K-groups of its universal C
*-algebra are shown to coincide with their classical counterparts. The U(1)-action on
......
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