1,523 research outputs found
Homological Epimorphisms of Differential Graded Algebras
Let R and S be differential graded algebras. In this paper we give a
characterisation of when a differential graded R-S-bimodule M induces a full
embedding of derived categories M\otimes - :D(S)--> D(R). In particular, this
characterisation generalises the theory of Geigle and Lenzing's homological
epimorphisms of rings. Furthermore, there is an application of the main result
to Dwyer and Greenlees's Morita theory.Comment: 14 page
Natural Associativity and Commutativity
Paper presented in three lectures in Anderson Hall on September 23, 24, 26, 196
Coherence of Associativity in Categories with Multiplication
The usual coherence theorem of MacLane for categories with multiplication
assumes that a certain pentagonal diagram commutes in order to conclude that
associativity isomorphisms are well defined in a certain practical sense. The
practical aspects include creating associativity isomorphisms from a given one
by tensoring with the identity on either the right or the left. We show, by
reinspecting MacLane's original arguments, that if tensoring with the identity
is restricted to one side, then the well definedness of constructed
isomorphisms follows from naturality only, with no need of the commutativity of
the pentagonal diagram. This observation was discovered by noting the
resemblance of the usual coherence theorems with certain properties of a
finitely presented group known as Thompson's group F. This paper is to be taken
as an advertisement for this connection.Comment: 8 pages, to appear in Journal of Pure and Applied Algebr
Self-duality of Selmer groups
The first part of the paper gives a new proof of self-duality for Selmer
groups: if A is an abelian variety over a number field K, and F/K is a Galois
extension with Galois group G, then the Q_pG-representation naturally
associated to the p-infinity Selmer group of A/F is self-dual. The second part
describes a method for obtaining information about parities of Selmer ranks
from the local Tamagawa numbers of A in intermediate extensions of F/K.Comment: 12 pages; to appear in Proc. Cam. Phil. So
Two polygraphic presentations of Petri nets
This document gives an algebraic and two polygraphic translations of Petri
nets, all three providing an easier way to describe reductions and to identify
some of them. The first one sees places as generators of a commutative monoid
and transitions as rewriting rules on it: this setting is totally equivalent to
Petri nets, but lacks any graphical intuition. The second one considers places
as 1-dimensional cells and transitions as 2-dimensional ones: this translation
recovers a graphical meaning but raises many difficulties since it uses
explicit permutations. Finally, the third translation sees places as
degenerated 2-dimensional cells and transitions as 3-dimensional ones: this is
a setting equivalent to Petri nets, equipped with a graphical interpretation.Comment: 28 pages, 24 figure
On the weak order of Coxeter groups
This paper provides some evidence for conjectural relations between
extensions of (right) weak order on Coxeter groups, closure operators on root
systems, and Bruhat order. The conjecture focused upon here refines an earlier
question as to whether the set of initial sections of reflection orders,
ordered by inclusion, forms a complete lattice. Meet and join in weak order are
described in terms of a suitable closure operator. Galois connections are
defined from the power set of W to itself, under which maximal subgroups of
certain groupoids correspond to certain complete meet subsemilattices of weak
order. An analogue of weak order for standard parabolic subsets of any rank of
the root system is defined, reducing to the usual weak order in rank zero, and
having some analogous properties in rank one (and conjecturally in general).Comment: 37 pages, submitte
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