Showing papers on "Free algebra published in 1990"
TL;DR: In this article, the free field representation for Wess-Zumino-Witten model with arbitrary Kac-Moody algebra and arbitrary central charge is discussed, and the special role of βγ systems is emphasized.
Abstract: The free field representation or "bosonization" rule1 for Wess-Zumino-Witten model (WZWM) with arbitrary Kac-Moody algebra and arbitrary central charge is discussed. Energy-momentum tensor, arising from Sugawara construction, is quadratic in the fields. In this way, all known formulae for conformal blocks and correlators may be easily reproduced as certain linear combinations of correlators of these free fields. Generalization to conformal blocks on arbitrary Riemann surfaces is straightforward. However, projection rules in the spirit of Ref. 2 are not specified. The special role of βγ systems is emphasized. From the mathematical point of view, the construction involved represents generators of Kac-Moody (KM) algebra in terms of generators of a Heisenberg one. If WZW Lagrangian is considered as d−1 of Kirillov form on an orbit of KM algebra,3 then the free fields of interest (i.e. generators of the Heisenberg algebra) diagonalize Kirillov form and the action. Reduction of KM algebra within the same construction should naturally lead to arbitrary coset models.
237 citations
01 Jan 1990
TL;DR: A subrecursive hierarchy {T n}n is defined which does not separate polynomial from exponential numeric functions, but does, based on nesting depth of a newly defined tiered recurrence.
Abstract: As a contribution to ongoing research on computing over general algebraic structures, we consider subrecurrence over free algebras Since the natural sub-recursive classification of functions by recurrence-nesting depth fails to separate polynomial from exponential numeric functions, we define a subrecursive hierarchy {T n }n which does, based on nesting depth of a newly defined tiered recurrence
43 citations
TL;DR: In this article, a monad on the category of compact spaces is constructed; it is defined by the inclusion hyperspace functor, and a characterization of the free algebras is given.
Abstract: A monad (in the Eilenberg-Moore sense) on the category of compact spaces is constructed; it is defined by the inclusion hyperspace functor. The category of algebras of this monad is described and a characterization of the free algebras is given.
13 citations
TL;DR: In this article, it was shown that if A is an arbitrary commutative ring and rank P>dimA[X 1,…,Xn]−n, then P is free.
5 citations
TL;DR: In this article, the Artin-Procesi theorem was generalized to the case of verbal prime algebras, and it was shown that all verbally prime p.i.
3 citations
01 Jan 1990
TL;DR: In this article, the authors discuss recent results concerning free algebraic systems and mention some old results which motivated them, and the selection of topics is eclectic and personal but with a special emphasis on results of a combinatorial nature.
Abstract: In this survey paper I discuss recent results concerning free algebraic systems and I mention some old results which motivated them. There is no attempt to be comprehensive. The selection of topics is eclectic and personal but with a special emphasis on results of a combinatorial nature.
2 citations
TL;DR: For a unary algebra A with k ≥ 2 fundamental operations, the class of all unary algebras that have a homomorphisrn into A, and the classQ(A) consist of all algesbras having A as one of their quotients are shown to be categorically universal if and only if either class contains a rigid algebra.
Abstract: For a unary algebraA withκ≥2 fundamental operations, letH(A) denote the class of all unary algebras that have a homomorphisrn intoA, and let the classQ(A) consist of all algebras havingA as one of their quotients. IfA is freely indecomposable then H(A) andQ(A) are shown to be categorically universal if and only if either class contains a rigid algebra; this, in turn, is equivalent to the absence of homomorphisms fromA into a free algebra.
1 citations