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FACTORING TILTING MODULES FOR ALGEBRAIC GROUPS
, 2009
"... Abstract. Let G be a semisimple, simplyconnected algebraic group over an algebraically closed field of characteristic p> 0. We observe that the tensor product of the Steinberg module with a minuscule module is always indecomposable tilting. Although quite easy to prove, this fact does not seem t ..."
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Abstract. Let G be a semisimple, simplyconnected algebraic group over an algebraically closed field of characteristic p> 0. We observe that the tensor product of the Steinberg module with a minuscule module is always indecomposable tilting. Although quite easy to prove, this fact does not seem
Algebraic structures on modules of diagrams
 Universit e Paris VII
, 1995
"... There exists a graded algebra Λ acting in a natural way on many modules of 3valent diagrams. Every simple Lie superalgebra with a nonsingular invariant bilinear form induces a character on Λ. The classical and exceptional Lie algebras and the Lie superalgebra D(2, 1, α) produce eight distinct chara ..."
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Cited by 29 (0 self)
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There exists a graded algebra Λ acting in a natural way on many modules of 3valent diagrams. Every simple Lie superalgebra with a nonsingular invariant bilinear form induces a character on Λ. The classical and exceptional Lie algebras and the Lie superalgebra D(2, 1, α) produce eight distinct
Typeful programming
, 1989
"... There exists an identifiable programming style based on the widespread use of type information handled through mechanical typechecking techniques. This typeful programming style is in a sense independent of the language it is embedded in; it adapts equally well to functional, imperative, objectorie ..."
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Cited by 151 (2 self)
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of modules, and very large programs, made of collections of large programs. We also sketch how typing applies to system programming; an area which by nature escapes rigid typing. In summary, we compare the most common programming styles, suggesting that many of them are compatible with, and benefit from, a
The Carlitz algebras
"... The Carlitz Fqalgebra C = Cν, ν ∈ N, is generated by an algebraically closed field K (which contains a nondiscrete locally compact field of positive characteristic p> 0, i.e. K ≃ Fq[[x,x −1]], q = p ν), by the (power of the) Frobenius map X = Xν: f ↦ → f q, and by the Carlitz derivative Y = Yν. ..."
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Cited by 9 (4 self)
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. It is proved that the Krull and global dimensions of C are 2, a classification of simple Cmodules and ideals are given, there are only countably many ideals, they commute (IJ = JI), and each ideal is a unique product of maximal ones. It is a remarkable fact that any simple Cmodule is a sum of eigenspaces
Baby Verma modules for rational Cherednik algebras
 Bull. London Math. Soc
"... Abstract. Symplectic reflection algebras arise in many different mathematical disciplines: integrable systems, Lie theory, representation theory, differential operators, symplectic geometry. In this paper, we introduce baby Verma modules for symplectic reflection algebras of complex reflection group ..."
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Cited by 57 (9 self)
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Abstract. Symplectic reflection algebras arise in many different mathematical disciplines: integrable systems, Lie theory, representation theory, differential operators, symplectic geometry. In this paper, we introduce baby Verma modules for symplectic reflection algebras of complex reflection
HZalgebra spectra are differential graded algebras
 Amer. Jour. Math
, 2004
"... Abstract: We show that the homotopy theory of differential graded algebras coincides with the homotopy theory of HZalgebra spectra. Namely, we construct Quillen equivalences between the Quillen model categories of (unbounded) differential graded algebras and HZalgebra spectra. We also construct Qu ..."
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Cited by 62 (13 self)
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Quillen equivalences between the differential graded modules and module spectra over these algebras. We use these equivalences in turn to produce algebraic models for rational stable model categories. We show that bascially any rational stable model category is Quillen equivalent to modules over a
Crosslayer congestion control, routing and scheduling design in ad hoc wireless networks
 PROC. IEEE INFOCOM
, 2006
"... This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless ..."
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Cited by 151 (10 self)
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channels (or singlerate wireless devices that can mask channel variations) as a utility maximization problem with these constraints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through
SUPERATOMIC BOOLEAN ALGEBRAS: MAXIMAL RIGIDITY
"... Abstract. We prove that for any superatomic Boolean Algebra of cardinality> ℶ4 there is an automorphism moving uncountably many atoms. Similarly for larger cardinals. Any of those results are essentially best possible Annotated Content §1 Superatomic Boolean algebras have nontrivial automorphisms ..."
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Abstract. We prove that for any superatomic Boolean Algebra of cardinality> ℶ4 there is an automorphism moving uncountably many atoms. Similarly for larger cardinals. Any of those results are essentially best possible Annotated Content §1 Superatomic Boolean algebras have nontrivial
Deo/nitions: operads, algebras and modules
 Contemporary Mathematics 202
, 1997
"... There are many different types of algebra: associative, associative and commutative, Lie, Poisson, etc., etc. Each comes with an appropriate notion of a module. As is becoming more and more important in a variety of fields, it is often necessary to deal with algebras and modules of these sorts “up t ..."
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Cited by 32 (3 self)
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There are many different types of algebra: associative, associative and commutative, Lie, Poisson, etc., etc. Each comes with an appropriate notion of a module. As is becoming more and more important in a variety of fields, it is often necessary to deal with algebras and modules of these sorts “up
Finite regularity and Koszul algebras
 Amer. J. Math
"... ABSTRACT: We determine the positively graded commutative algebras over which the residue field modulo the homogeneous maximal ideal has finite CastelnuovoMumford regularity: they are the polynomial rings in finitely many indeterminates over Koszul algebras; this proves a conjecture in [3]. We also ..."
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Cited by 22 (2 self)
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ABSTRACT: We determine the positively graded commutative algebras over which the residue field modulo the homogeneous maximal ideal has finite CastelnuovoMumford regularity: they are the polynomial rings in finitely many indeterminates over Koszul algebras; this proves a conjecture in [3]. We also
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