2,154 research outputs found
Investigating self-similar groups using their finite -presentation
Self-similar groups provide a rich source of groups with interesting
properties; e.g., infinite torsion groups (Burnside groups) and groups with an
intermediate word growth. Various self-similar groups can be described by a
recursive (possibly infinite) presentation, a so-called finite
-presentation. Finite -presentations allow numerous algorithms for
finitely presented groups to be generalized to this special class of recursive
presentations. We give an overview of the algorithms for finitely -presented
groups. As applications, we demonstrate how their implementation in a computer
algebra system allows us to study explicit examples of self-similar groups
including the Fabrykowski-Gupta groups. Our experiments yield detailed insight
into the structure of these groups
Coordinates and Automorphisms of Polynomial and Free Associative Algebras of Rank Three
We study z-automorphisms of the polynomial algebra K[x,y,z] and the free
associative algebra K over a field K, i.e., automorphisms which fix the
variable z. We survey some recent results on such automorphisms and on the
corresponding coordinates. For K we include also results about the
structure of the z-tame automorphisms and algorithms which recognize z-tame
automorphisms and z-tame coordinates
A constructive method for decomposing real representations
A constructive method for decomposing finite dimensional representations of
semisimple real Lie algebras is developed. The method is illustrated by an
example. We also discuss an implementation of the algorithm in the language of
the computer algebra system {\sf GAP}4.Comment: Final version; to appear in "Journal of Symbolic Computation
Ricci Nilsoliton Black Holes
We follow a constructive approach and find higher-dimensional black holes
with Ricci nilsoliton horizons. The spacetimes are solutions to Einstein's
equation with a negative cosmological constant and generalises therefore,
anti-de Sitter black hole spacetimes. The approach combines a work by Lauret --
which relate so-called Ricci nilsolitons and Einstein solvmanifolds -- and an
earlier work by the author. The resulting black hole spacetimes are
asymptotically Einstein solvmanifolds and thus, are examples of solutions which
are not asymptotically Anti-de Sitter. We show that any nilpotent group in
dimension has a corresponding Ricci nilsoliton black hole solution in
dimension (n+2). Furthermore, we show that in dimensions (n+2)>8, there exists
an infinite number of locally distinct Ricci nilsoliton black hole metrics.Comment: 19 pages; fixed formatting problem
- …