Archive for December, 2003
Contents of Volume 6 (2003)
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DOI: 10.1023/B:ALGE.0000006624.59223.a3
Print publication date: 12/1/2003
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Division Algebras that Ramify only on a Plane Quartic Curve with Simply Connected Components
by Ford, T. J.
A central division algebra Λ over the field of rational functions in two variables with coefficients over an algebraically closed field ramifies along a divisor on P
2. If the ramification divisor of Λ is a quartic curve which is the union of simply connected curves, we show that Λ is a symbol algebra and satisfies the ‘index equals exponent’ equation.
DOI: 10.1023/B:ALGE.0000006494.31777.00
Print publication date: 12/1/2003
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The p-Blocks of the Mackey Algebra
by Bouc, Serge
Let p be a prime number. This paper describes the primitive idempotents and prime spectrum of the crossed Burnside algebra of a finite group over a p-local ring. The main application is a formula for the block idempotents of the p-local Mackey algebra of the group, in terms of the corresponding bloks of the group algebra.
DOI: 10.1023/B:ALGE.0000006493.77655.e5
Print publication date: 12/1/2003
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Coherent Functors and Covariantly Finite Subcategories
by Krause, Henning
Given a locally presentable additive category A, we study a class of covariantly finite subcategories which we call definable. A definable subcategory arises from a set of coherent functors F
i
on A by taking all objects X in A such that F
i
X=0 for all i. We give various characterizations of definable subcategories, demonstrating that all covariantly finite subcategories which arise in practice are of this form. This is based on a filtration of the category of all coherent functors on A.
DOI: 10.1023/B:ALGE.0000006492.02381.df
Print publication date: 12/1/2003
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Finite-Dimensional Algebras and Standard Systems
by Du, Jie
We introduce the notion of a standard system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for a finite-dimensional algebra to be quasi-hereditary is the existence of a full and divisible standard system. As a further application, we obtain a sufficient condition for a standardly stratified algebra.
DOI: 10.1023/B:ALGE.0000006491.28617.d8
Print publication date: 12/1/2003
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