30,743 research outputs found
Generic Trace Semantics via Coinduction
Trace semantics has been defined for various kinds of state-based systems,
notably with different forms of branching such as non-determinism vs.
probability. In this paper we claim to identify one underlying mathematical
structure behind these "trace semantics," namely coinduction in a Kleisli
category. This claim is based on our technical result that, under a suitably
order-enriched setting, a final coalgebra in a Kleisli category is given by an
initial algebra in the category Sets. Formerly the theory of coalgebras has
been employed mostly in Sets where coinduction yields a finer process semantics
of bisimilarity. Therefore this paper extends the application field of
coalgebras, providing a new instance of the principle "process semantics via
coinduction."Comment: To appear in Logical Methods in Computer Science. 36 page
Traces in braided categories
With any even Hecke symmetry R (that is a Hecke type solution of the
Yang-Baxter equation) we associate a quasitensor category. We formulate a
condition on R implying that the constructed category is rigid and its
commutativity isomorphisms R_{U,V} are natural. We show that this condition
leads to rescaling of the initial Hecke symmetry. We suggest a new way of
introducing traces as properly normalized categorical morphisms End(V) --> K
and deduce the corresponding normalization from categorical dimensions.Comment: Source: Revised version, a more attention is given to the problem of
trace definition and its proper normalization in braided categories with
Hecke type braidings. Minor corrections in Introduction. LaTex file, all
macros included, no figure
The extended Bloch group and algebraic K-theory
We define an extended Bloch group for an arbitrary field F, and show that
this group is canonically isomorphic to K_3^ind(F) if F is a number field. This
gives an explicit description of K_3^ind(F) in terms of generators and
relations. We give a concrete formula for the regulator, and derive concrete
symbol expressions generating the torsion. As an application, we show that a
hyperbolic 3-manifold with finite volume and invariant trace field k has a
fundamental class in K_3^ind(k) tensor Z[1/2].Comment: 32 pages, 5 figure
Algebraic Independence in SL(3,C) Character Varieties of Free Groups
Let X be the moduli space of SL(3,C) representations of a free group of rank
r. In this paper we describe maximal algebraically independent subsets of
certain minimal sets of coordinate functions on X. These subsets locally
parametrize the moduli space.Comment: 13 pages, v2 contains minor change
- …