For the associative algebra A(g) of an infinite-dimensional Lie g, we introduce twisted fiber bundles over arbitrary compact topological spaces. Fibers such are given by elements algebraic completion space formal series in complex parameters, sections provided rational functions with prescribed analytic properties. Homotopical invariance as well covariance terms trivial A(g)-bundles is proven. ...

ĉ = 1 fermionic string theory, which is considered as a fermionic string theory in two dimension, is shown to decompose into two mutually independent parts, one of which can be viewed as a topological model and the other is irrelevant for the theory. The physical contents of the theory is largely governed by this topological structure, and the discrete physical spectrum of ĉ = 1 string theory i...

Sufficient conditions for a topological ∗-algebra under which several Hermitian inner products are mutually equivalent are given.

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective we develop a more general approach to sofic entropy which produces both measure and topological dynamical invariants, and we establish the variational princi...

Let AR(D) denote the set of functions belonging to the disc algebra having real Fourier coefficients. We show that AR(D) has Bass and topological stable ranks equal to 2, which settles the conjecture made by Brett Wick in [18]. We also give a necessary and sufficient condition for reducibility in some real algebras of functions on symmetric domains with holes, which is a generalization of the m...

We write down one-to-one mappings between the singular vectors of the Neveu-Schwarz N=2 superconformal algebra and 16 + 16 types of singular vectors of the Topological and of the Ramond N=2 superconformal algebras. As a result one obtains construction formulae for the latter using the construction formulae for the Neveu-Schwarz singular vectors due to Dörrzapf. The indecomposable singular vecto...

Suppose G is a second countable, locally compact, Hausdorff groupoid with a fixed left Haar system. Let G/G denote the orbit space of G and C∗(G) denote the groupoid C∗-algebra. Suppose that G is a principal groupoid. We show that C∗(G) is CCR if and only if G/G is a T1 topological space, and that C∗(G) is GCR if and only if G/G is a T0 topological space. We also show that C∗(G) is a Fell Algeb...

Visualization is the discipline in Computer Science dealing with the representation of data by computer generated images. “It transforms the symbolic into the geometric, enabling researchers to observe their simulations and computations,” [MD87, p. 2]. One major area visualizes vector fields. In applied mathematics, the study of gas dynamics, combustion and fluid flow leads to vector fields des...

The cocycle approach to topological charge algebras is generalized to the case of D-branes. The D-brane has two associated cocycles, with an anomalous term of the Noether charge algebra deriving from each. The resulting topological charge algebras are extensions of the standard, background superalgebra by two disjoint, commuting ideals. The formalism is applied to (p, q)-strings and the D-membr...