A Norm Map for Endomorphism Algebras of Gelfand-Graev Representations

For any positive integer n, we construct an n-repetitive generalized cluster complex (a simplicial complex) associated with a given finite root system by defining a compatibility degree on the n-repetitive set of the colored root system. This simplicial complex includes Fomin-Reading's generalized cluster complex as a special case when n=1. We also introduce the intermediate coverings (called generalized d-cluster categories) of d-cluster categories of hereditary algebras, and study the d-cluster tilting objects and their endomorphism algebras in those categories. In particular, we show that the endomorphism algebras of d-cluster tilting objects in the generalized d-cluster categories provide the (finite) coverings of the corresponding (usual) d-cluster tilted algebras. Moreover, we prove that the generalized d-cluster categories of hereditary algebras of finite representation type provide a category model for the n-repetitive generalized cluster complexes.

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Endomorphism algebras of large modules with distinguished submodules

Journal of Algebra ◽

10.1016/0021-8693(69)90052-0 ◽

1969 ◽

Vol 11 (2) ◽

pp. 155-185 ◽

Cited By ~ 51

Author(s):

A.L.S Corner

Keyword(s):

Endomorphism Algebras

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Endomorphism Algebras of Abelian Varieties

Algebraic Geometry and Commutative Algebra ◽

10.1016/b978-0-12-348032-3.50007-4 ◽

1988 ◽

pp. 469-502 ◽

Cited By ~ 7

Author(s):

Frans OORT

Keyword(s):

Abelian Varieties ◽

Endomorphism Algebras

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Quasi-Hereditary Endomorphism Algebras

Canadian Mathematical Bulletin ◽

10.4153/cmb-1995-061-3 ◽

1995 ◽

Vol 38 (4) ◽

pp. 421-428 ◽

Cited By ~ 4

Author(s):

V. Dlab ◽

P. Heath ◽

F. Marko

Keyword(s):

Lie Algebras ◽

Algebraic Groups ◽

Simple Complex ◽

Highest Weight ◽

Endomorphism Algebras ◽

Hereditary Algebras ◽

Highest Weight Categories

AbstractQuasi-hereditary algebras were introduced by Cline-Parshall-Scott (see [CPS] or [PS]) to deal with highest weight categories which occur in the study of semi-simple complex Lie algebras and algebraic groups. In fact, the quasi-hereditary algebras which appear in these applications enjoy a number of additional properties. The objective of this brief note is to describe a class of lean quasi-hereditary algebras [ADL] which possess such typical characteristics. A study of these questions originated in collaboration with C. M. Ringel (see [DR]).

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The structure theorem and duality theorem for endomorphism algebras of weak Hopf group coalgebras

Journal of Algebra and Its Applications ◽

10.1142/s0219498817502085 ◽

2017 ◽

Vol 16 (11) ◽

pp. 1750208

Author(s):

Ling Jia

Keyword(s):

Duality Theorem ◽

Structure Theorem ◽

Weak Group ◽

Endomorphism Algebras ◽

Hopf Formula ◽

Hopf Modules ◽

Homological Algebras

In this paper, we investigate the HOM-functor and state the structure theorem for endomorphism algebras of weak two-sided [Formula: see text]-Hopf [Formula: see text]-modules in order to explore homological algebras for weak Hopf [Formula: see text]-modules, and present the duality theorem for weak group “big” Smash products which extends the result of Menini and Raianu [Morphisms of relative Hopf modules, Smash products and duality, J. Algebra 219 (1999) 547–570] in the setting of weak Hopf group coalgebras.

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