Compact Elements and Smallest Faithful Representation of C ∗ -Algebras

The Smallest Faithful Representation of a Certain Extension of Sl2

LetG be the six dimensional linear algebraic k-group SL2(W2), where W2 is the ring of Witt vectors of length two over the algebraically closed field k of characteristic p > 0. Then the minimal dimension of a faithful rational krepresentation of G is p + 3.

Associative Conformal Algebras with Finite Faithful Representation

The notion of conformal algebra appears as an algebraical language describing singular part of operator product expansion (OPE) in conformal field theory [BPZ]. Explicit algebraical exposition of this theory leads to the notion of vertex (chiral) algebra (see, e.g., [B], [DL], [FLM]). Roughly speaking, conformal algebras correspond to vertex algebras by the same way as Lie algebras correspond t...

Representation of faithful normal expectations in von Neumann algebras

A Faithful Representation of Temperley-Lieb Algebras in Matrices

It is shown that Temperley-Lieb algebras in which the multiplicative generators satisfy hihi = nhi for n ≥ 2 can be isomorphically represented in matrices. Mathematics Subject Classification (2000): 57M99, 15A03, 16G99, 05C50

Representation Theory of Analytic Holonomy C Algebras

Integral calculus on the space A/G of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well–suited for quantization of diffeomorphism invariant theories of connections. The general setting is provided by the abelian C–algebra of functions on A/G generated by Wilson loops (i.e., by the traces of holonomies of conn...