7,247 research outputs found
The foundational legacy of ASL
Abstract. We recall the kernel algebraic specification language ASL and outline its main features in the context of the state of research on algebraic specification at the time it was conceived in the early 1980s. We discuss the most significant new ideas in ASL and the influence they had on subsequent developments in the field and on our own work in particular.
A Hopf laboratory for symmetric functions
An analysis of symmetric function theory is given from the perspective of the
underlying Hopf and bi-algebraic structures. These are presented explicitly in
terms of standard symmetric function operations. Particular attention is
focussed on Laplace pairing, Sweedler cohomology for 1- and 2-cochains, and
twisted products (Rota cliffordizations) induced by branching operators in the
symmetric function context. The latter are shown to include the algebras of
symmetric functions of orthogonal and symplectic type. A commentary on related
issues in the combinatorial approach to quantum field theory is given.Comment: 29 pages, LaTeX, uses amsmat
Subalgebras of FA-presentable algebras
Automatic presentations, also called FA-presentations, were introduced to
extend finite model theory to infinite structures whilst retaining the
solubility of fundamental decision problems. This paper studies FA-presentable
algebras. First, an example is given to show that the class of finitely
generated FA-presentable algebras is not closed under forming finitely
generated subalgebras, even within the class of algebras with only unary
operations. However, it is proven that a finitely generated subalgebra of an
FA-presentable algebra with a single unary operation is itself FA-presentable.
Furthermore, it is proven that the class of unary FA-presentable algebras is
closed under forming finitely generated subalgebras, and that the membership
problem for such subalgebras is decidable.Comment: 19 pages, 6 figure
Homology and Cohomology of E-infinity Ring Spectra
Every homology or cohomology theory on a category of E-infinity ring spectra
is Topological Andre-Quillen homology or cohomology with appropriate
coefficients. Analogous results hold for the category of A-infinity ring
spectra and for categories of algebras over many other operads
The Multiplication on BP
BP is an E_4 ring spectrum. The E_4 structure is unique up to automorphism
V.M. Miklyukov: from dimension 8 to nonassociative algebras
In this short survey we give a background and explain some recent
developments in algebraic minimal cones and nonassociative algebras. A good
deal of this paper is recollections of my collaboration with my teacher, PhD
supervisor and a colleague, Vladimir Miklyukov on minimal surface theory that
motivated the present research. This paper is dedicated to his memory.Comment: 19 page
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