3,714 research outputs found
Left-symmetric algebras, or pre-Lie algebras in geometry and physics
In this survey article we discuss the origin, theory and applications of
left-symmetric algebras (LSAs in short) in geometry in physics. Recently
Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics
(QFT and renormalization theory), where the name pre-Lie algebras is used quite
often. Already Cayley wrote about such algebras more than hundred years ago.
Indeed, LSAs arise in many different areas of mathematics and physics. We
attempt to give a survey of the fields where LSAs play an important role.
Furthermore we study the algebraic theory of LSAs such as structure theory,
radical theory, cohomology theory and the classification of simple LSAs. We
also discuss applications to faithful Lie algebra representations.Comment: 28 pages, 3 figure
Towards an ASM thesis for reflective sequential algorithms
Starting from Gurevich's thesis for sequential algorithms (the so-called
"sequential ASM thesis"), we propose a characterization of the behaviour of
sequential algorithms enriched with reflection. That is, we present a set of
postulates which we conjecture capture the fundamental properties of reflective
sequential algorithms (RSAs). Then we look at the plausibility of an ASM thesis
for the class of RSAs, defining a model of abstract state machine (which we
call reflective ASM) that we conjecture captures the class of RSAs as defined
by our postulates
On Cellular Algebras with Jucys Murphy Elements
We study analogues of Jucys-Murphy elements in cellular algebras arising from
repeated Jones basic constructions. Examples include Brauer and BMW algebras
and their cyclotomic analogues.Comment: Improved and reorganized exposition. Some new result
- …