Algebras and Representation Theory
Công bố khoa học tiêu biểu
* Dữ liệu chỉ mang tính chất tham khảo
Sắp xếp:
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 $\mathfrak {sl}_{n+1}$ having highest weight
multiple of fu...
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 the basis $\mathfrak {B}^{\prime } = \{w_{j}\}_{j \in J}$ of 𝕎 if
for any $\sigma \in S_{n}, i_{1},\dots ,i_{k} \in I$ and $j_{k + 1},\dots ,
j_{n} \in J$ ...
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 $\mathfrak {R}(A)=\oplus _{(g,h)\in G\times
H}A_{(g,h)}\otimes R_{h}$ . In this paper we provide a basis for the graded
identitie...
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
cas...
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 $\mathcal{O}(S^{3}_{pq})$
corresponding for p=1=q to the classical Hopf fibration is proven to be Galois
(free). The thus obt...
Brauer–Thrall for Totally Reflexive Modules over Local Rings of Higher Dimension
Algebras and Representation Theory - Tập 17 - Trang 997-1008 - 2013
Let R be a commutative Noetherian local ring. Assume that R has a pair {x,y} of
exact zerodivisors such that dim R/(x,y) ≥ 2 and all totally reflexive
R/(x)-modules are free. We show that the first and second Brauer–Thrall type
theorems hold for the category of totally reflexive R-modules. More precisely,
we prove that, for infinitely many integers n, there exists an indecomposable
totally reflexi...
Tổng số: 967
- 1
- 2
- 3
- 4
- 5
- 6
- 10