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301
Noether numbers for subrepresentations of cyclic groups of prime order
 BULL. LONDON MATH. SOC
, 2002
"... Let W be a finitedimensional �/pmodule over a field, k, of characteristic p. The maximum degree of an indecomposable element of the algebra of invariants, k[W] �/p, is called the Noether number of the representation, and is denoted by β(W). A lower bound for β(W) is derived, and it is shown that i ..."
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Cited by 12 (10 self)
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Let W be a finitedimensional �/pmodule over a field, k, of characteristic p. The maximum degree of an indecomposable element of the algebra of invariants, k[W] �/p, is called the Noether number of the representation, and is denoted by β(W). A lower bound for β(W) is derived, and it is shown
FINITEDIMENSIONAL REPRESENTATIONS OF HYPER LOOP ALGEBRAS
, 2007
"... Abstract: We study finitedimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finitedimensional simple Lie algebra. The main results are the classification of the irre ..."
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Cited by 8 (5 self)
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Abstract: We study finitedimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finitedimensional simple Lie algebra. The main results are the classification
FINITEDIMENSIONAL ALGEBRAS WITH SMALLEST RESOLUTIONS OF SIMPLE MODULES
, 2005
"... Let Λ be an associative ring with identity and with the Jacobson radical r, let mod Λ be the category of finitely generated left Λmodules, and let Λ op be the opposite ring of Λ. All modules are left unital modules, and if X is a module then pdX is the projective dimension of X. If Λ is left artini ..."
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Let Λ be an associative ring with identity and with the Jacobson radical r, let mod Λ be the category of finitely generated left Λmodules, and let Λ op be the opposite ring of Λ. All modules are left unital modules, and if X is a module then pdX is the projective dimension of X. If Λ is left
NOTES ON THE DRINFELD DOUBLE OF FINITEDIMENSIONAL GROUP ALGEBRAS
"... Abstract. Let k be an algebraically closed field of characteristic p> 0. We characterize the finite groups G for which the Drinfeld double D(kG) of the group algebra kG has the Chevalley property. We also show that this is the case if and only if the tensor product of every simple D(kG)module wi ..."
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Abstract. Let k be an algebraically closed field of characteristic p> 0. We characterize the finite groups G for which the Drinfeld double D(kG) of the group algebra kG has the Chevalley property. We also show that this is the case if and only if the tensor product of every simple D(kG)module
7 Structure of finite dimensional algebras
"... In this section we return to studying the structure of finite dimensional algebras. Throughout the section, we work over an algebraically closed field k (of any characteristic). 7.1 Projective modules Let A be an algebra, and P be a left Amodule. Theorem 7.1. The following properties of P are equiv ..."
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In this section we return to studying the structure of finite dimensional algebras. Throughout the section, we work over an algebraically closed field k (of any characteristic). 7.1 Projective modules Let A be an algebra, and P be a left Amodule. Theorem 7.1. The following properties of P
Representations of Finite Dimensional Hopf Algebras
"... . Let H denote a finite dimensional Hopf algebra with antipode S over a field . We give a new proof of the fact, due to Oberst and Schneider [OS], that H is a symmetric algebra if and only if H is unimodular and S 2 is inner. If H is involutory and not semisimple, then the dimensions of all p ..."
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Cited by 2 (0 self)
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. Let H denote a finite dimensional Hopf algebra with antipode S over a field . We give a new proof of the fact, due to Oberst and Schneider [OS], that H is a symmetric algebra if and only if H is unimodular and S 2 is inner. If H is involutory and not semisimple, then the dimensions of all
Viewing Finite Dimensional Representations Through Infinite Dimensional Ones
, 1999
"... this article. Namely, for the finite dimensional monomial FINITE VERSUS INFINITE DIMENSIONAL REPRESENTATIONS 87 relation algebra of [8] with l fin dim ! l Fin dim , we exhibit a simple leftmodule which fails to have a P ..."
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Cited by 6 (3 self)
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this article. Namely, for the finite dimensional monomial FINITE VERSUS INFINITE DIMENSIONAL REPRESENTATIONS 87 relation algebra of [8] with l fin dim ! l Fin dim , we exhibit a simple leftmodule which fails to have a P
Finite dimensional modules for rational Cherednik algebras
, 2006
"... We construct and study some finite dimensional modules for rational Cherednik algebras for the groups G(r, p, n) by using intertwining operators and a commutative family of operators introduced by Dunkl and Opdam. The coinvariant ring and an analog of the ring constructed by Gordon in the course of ..."
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Cited by 5 (3 self)
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We construct and study some finite dimensional modules for rational Cherednik algebras for the groups G(r, p, n) by using intertwining operators and a commutative family of operators introduced by Dunkl and Opdam. The coinvariant ring and an analog of the ring constructed by Gordon in the course
THE GENERATING HYPOTHESIS FOR THE STABLE MODULE CATEGORY of a pGroup
, 2006
"... of a finite pgroup G, is the statement that a map between finitedimensional kGmodules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd’s generating hypothesis holds for a nontrivial finite pgroup G if and only if G is either C2 or C3. We also giv ..."
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Cited by 16 (6 self)
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of a finite pgroup G, is the statement that a map between finitedimensional kGmodules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd’s generating hypothesis holds for a nontrivial finite pgroup G if and only if G is either C2 or C3. We also
Results 1  10
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301