2,083 research outputs found
Logspace computations in graph products
We consider three important and well-studied algorithmic problems in group
theory: the word, geodesic, and conjugacy problem. We show transfer results
from individual groups to graph products. We concentrate on logspace complexity
because the challenge is actually in small complexity classes, only. The most
difficult transfer result is for the conjugacy problem. We have a general
result for graph products, but even in the special case of a graph group the
result is new. Graph groups are closely linked to the theory of Mazurkiewicz
traces which form an algebraic model for concurrent processes. Our proofs are
combinatorial and based on well-known concepts in trace theory. We also use
rewriting techniques over traces. For the group-theoretical part we apply
Bass-Serre theory. But as we need explicit formulae and as we design concrete
algorithms all our group-theoretical calculations are completely explicit and
accessible to non-specialists
A Rational Logarithmic Conformal Field Theory
We analyse the fusion of representations of the triplet algebra, the
maximally extended symmetry algebra of the Virasoro algebra at c=-2. It is
shown that there exists a finite number of representations which are closed
under fusion. These include all irreducible representations, but also some
reducible representations which appear as indecomposable components in fusion
products.Comment: 10 pages, LaTe
On the free field realization of algebras
Defining the algebras as the commutant of certain screening charges a
special form for the classical generators is obtained which does not change
under quantisation. This enables us to give explicitly the first few generators
in a compact form for arbitrary algebras.Comment: 9 pages, Latex, reference added, to appear in Phys. Let.
W-algebras with set of primary fields of dimensions (3, 4, 5) and (3,4,5,6)
We show that that the Jacobi-identities for a W-algebra with primary fields
of dimensions 3, 4 and 5 allow two different solutions. The first solution can
be identified with WA_4. The second is special in the sense that, even though
associative for general value of the central charge, null-fields appear that
violate some of the Jacobi-identities, a fact that is usually linked to
exceptional W-algebras. In contrast we find for the algebra that has an
additional spin 6 field only the solution WA_5.Comment: 17 pages, LaTeX, KCL-TH-92-9, DFFT-70/9
- …