2,548 research outputs found
Vertex rings and their Pierce bundles
In part I we introduce vertex rings, which bear the same relation to vertex
algebras (or VOAs) as commutative, associative rings do to commutative,
associative algebras over the complex numbers. We show that vertex rings are
characterized by Goddard axioms. These include a generalization of the
translation-covariance axiom of VOA theory that involves a canonical
Hasse-Schmidt derivation naturally associated to any vertex ring. We give
several illustrative applications of these axioms, including the construction
of vertex rings associated with the Virasoro algebra. We consider some
categories of vertex rings, and the role played by the center of a vertex ring.
In part II we extend the theory of Pierce bundles associated to a commutative
ring to the setting of vertex rings. This amounts to the construction of
certain reduced etale bundles of vertex rings functorially associated to a
vertex ring. We introduce von Neumann regular vertex rings as a generalization
of von Neumann regular commutative rings; we obtain a characterization of this
class of vertex rings as those whose Pierce bundles are bundles of simple
vertex rings
Hypergroups and Hypergroup Algebras
The survey contains a brief description of the ideas, constructions, results,
and prospects of the theory of hypergroups and generalized translation
operators. Representations of hypergroups are considered, being treated as
continuous representations of topological hypergroup algebras.Comment: 52 page
Maximal C*-algebras of quotients and injective envelopes of C*-algebras
A new C*-enlargement of a C*-algebra nested between the local multiplier
algebra of and its injective envelope is
introduced. Various aspects of this maximal C*-algebra of quotients,
, are studied, notably in the setting of AW*-algebras. As a
by-product we obtain a new example of a type I C*-algebra such that
.Comment: 37 page
Prime ideals in nilpotent Iwasawa algebras
Let G be a nilpotent complete p-valued group of finite rank and let k be a
field of characteristic p. We prove that every faithful prime ideal of the
Iwasawa algebra kG is controlled by the centre of G, and use this to show that
the prime spectrum of kG is a disjoint union of commutative strata. We also
show that every prime ideal of kG is completely prime. The key ingredient in
the proof is the construction of a non-commutative valuation on certain
filtered simple Artinian rings
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