SU(∞), SU+(∞) and area-preserving algebras (original) (raw)

INFINITE-DIMENSIONAL ALGEBRAS, SINE BRACKETS, AND SU(∞)

We investigate features of the infinite dimensional algebras we have previously introduced, which involve trigonometric func- tions in their structure constants. We find a realization for them which leads to a basis-independent formulation. A special family of them, the cyclotomic ones, contain SU (N) as invariant subalgebras. In this basis, it is evident by inspection that the algebra of SU(or) is equivalent to the centerless algebra of SDiffoon two-dimensional manifolds. Gauge theories of SU(oo) are thus simply reformulated in terms of surface coordinates

ec 2 00 3 A utom orphism s ofassociative algebras and noncom m utative geom etry

2021

A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the h-deformed plane and the quantum group GL p,q (2) are recovered in this way. Geometric structures like metrics and compatible linear connections are introduced. 1 Let us consider a change of basis θ s → θ ′ s := s ′ ∈S U s s ′ θ s ′ where U is an invertible matrix with entries in A, or some extension of A. Then (1.1) holds with the substitution Φ(f) → Φ ′ (f) := U Φ(f) U −1. The problem is to find a U such that Φ ′ (f) is diagonal for all f ∈ A.

The topography of W∞-type algebras

Physics Letters B, 1993

We chart out the landscape of W ∞ -type algebras using W (q) KP -a recently discovered one-parameter deformation of W KP . We relate all hitherto known W ∞ -type algebras to W (q) KP and its reductions, contractions, and/or truncations at special values of the parameter. ♭

Algebras of infinitesimal CR automorphisms

Journal of Algebra, 2005

Set H + = H + (g, q) = (q + q) ∩ g = {Re Z | Z ∈ q}, where conjugation and real part, both here and in the following, are taken with respect to the real form g ofĝ. We call the quotient H = H(g, q) = H + /g + ⊂ T the analytic tangent space of (g, q).

F and M Theories as Gauge Theories of Area Preserving Algebra

F theory and M theory are formulated as gauge theories of area preserving diffeomorphism algebra. Our M theory is shown to be 1-brane formulation rather than 0-brane formulation of M theory of Banks, Fischler, Shenker and Susskind and the F theory is shown to be 1-brane formulation rather than -1-brane formulation of type IIB matrix theory of Ishibashi, Kawai, Kitazawa and Tsuchiya.

A universal enveloping for LinftyL_\inftyLinfty-algebras

Mathematical Research Letters, 2008

For any L∞-algebra L we construct an A∞-algebra structure on the symmetric coalgebra Sym * c (L) and prove that this structure satisfies properties generalizing those of the usual universal enveloping algebra. These properties follow from an invariant contracting homotopy one the cobar construction of an exterior coalgebra and its relation to combinatorics of permutahedra and semistandard Young tableaux.

On the symmetric enveloping algebra of planar algebra subfactors

Transactions of the American Mathematical Society, 2013

We give a diagrammatic description of Popa's symmetric enveloping algebras associated to planar algebra subfactors. As an application we construct a natural family of derivations on these factors, and compute a certain free entropy dimension type quantity.

Pre- and Post-Lie Algebras: The Algebro-Geometric View

Computation and Combinatorics in Dynamics, Stochastics and Control

We relate composition and substitution in pre-and post-Lie algebras to algebraic geometry. The Connes-Kreimer Hopf algebras, and MKW Hopf algebras are then coordinate rings of the infinite-dimensional affine varieties consisting of series of trees, resp. Lie series of ordered trees. Furthermore we describe the Hopf algebras which are coordinate rings of the automorphism groups of these varieties, which govern the substitution law in pre-and post-Lie algebras. Contents Introduction Part 1. The non-algebro geometric setting Date: date. 1 2 GUNNAR FLØYSTAD AND HANS MUNTHE-KAAS 5.3. Substitution 27 6. Action of the endomorphism group and substitution in free post-Lie algebras 28 6.1. A bialgebra of endomorphisms 28 6.2. The action on the free post-Lie algebra 29 6.3. The universal substitution 31 6.4. Recursion formula 33