Showing papers on "Algebra representation published in 1984"
TL;DR: In this article, the anomalous dimensions of the Wess-Zumino fields are found exactly, and the multipoint correlation functions are shown to satisfy linear differential equations, in particular, Witten's non-abelean bosonisation rules are proven.
1,793 citations
344 citations
TL;DR: A natural action of the Monster is obtained on V compatible with the action of [unk], thus conceptually explaining a major part of the numerical observations known as Monstrous Moonshine.
Abstract: We announce the construction of an irreducible graded module V for an “affine” commutative nonassociative algebra [unk]. This algebra is an “affinization” of a slight variant [unk] of the commutative nonassociative algebra B defined by Griess in his construction of the Monster sporadic group F1. The character of V is given by the modular function J(q) = q-1 + 0 + 196884q +.... We obtain a natural action of the Monster on V compatible with the action of [unk], thus conceptually explaining a major part of the numerical observations known as Monstrous Moonshine. Our construction starts from ideas in the theory of the basic representations of affine Lie algebras and develops further the calculus of vertex operators. In particular, the homogeneous and principal representations of the simplest affine Lie algebra A1(l) and the relation between them play an important role in our construction. As a corollary we deduce Griess's results, obtained previously by direct calculation, about the algebra structure of B and the action of F1 on it. In this work, the Monster, a finite group, is defined and studied by means of a canonical infinite-dimensional representation.
305 citations
TL;DR: The conformal algebra for operators of the Z3 model at the phase transition point is built in this article, where critical exponents are found in this approach as solutions of simple algebraic equations.
192 citations
180 citations
TL;DR: In this paper, the authors show how to compute the Kac determinant using well known techniques from dual models and discuss the validity of the no-ghost theorem of dual models in a more general setting than the original proofs of that theorem.
78 citations
01 Mar 1984
TL;DR: In this paper, it was shown that a locally compact group G is amenable iff each multiplier on the Fourier algebra A(G) is given by a function from B(G).
Abstract: It is shown that a locally compact group G is amenable iff each multiplier on the Fourier algebra A(G) is given by a function from the Fourier- Stieltjes algebra B(G) Another condition is that the norm of A(G) is equiv- alent to that induced by the regular representation of A(G)
66 citations
Journal Article•
TL;DR: This work introduces recursively defined processes and regular processes, both in presence and absence of communication, and introduces fixed point algebras which have useful applications in several proofs.
Abstract: We introduce recursively defined processes and regular processes, both in presence and absence of communication. It is shown that both classes are process algebras. As an example of recursively defined processes, Bag and Stack are discussed in detail. It is shown that Bag cannot be recursively defined without merge. We introduce fixed point algebras which have useful applications in several proofs.
63 citations
TL;DR: In this article, three modifications of the symmetric algebra of a module are introduced and their arithmetical and homological properties studied, and the main tools are certain fitting ideals of the module and an extension to modules of a complex of not necessarily free modules that have used in studying blowing-up rings.
Abstract: Three modifications of the symmetric algebra of a module are introduced and their arithmetical and homological properties studied. Emphasis is placed on converting syzygetic properties of the modules into ideal theoretic properties of the algebras, e.g. Cohen-Macaulayness, factoriality. The main tools are certain Fitting ideals of the module and an extension to modules of a complex of not necessarily free modules that we have used in studying blowing-up rings.
16 Jul 1984
TL;DR: In this paper, the authors introduce recursively defined processes and regular processes, both in presence and absence of communication, and show that both classes are process algebras.
Abstract: We introduce recursively defined processes and regular processes, both in presence and absence of communication. It is shown that both classes are process algebras. As an example of recursively defined processes, Bag and Stack are discussed in detail. It is shown that Bag cannot be recursively defined without merge. We introduce fixed point algebras which have useful applications in several proofs.
TL;DR: In this paper, it was shown that if L is a finite-width commutative subspace lattice and K is the set of compact operators, then the quasitriangular algebra Alg L + K is closed in the norm topology.
TL;DR: In this paper, a polygroup is introduced and used to establish connections among relation algebras, permutation groups, and edge-colored graphs, and a multivalued algebra is introduced.
Abstract: A multivalued algebra called a polygroup is introduced and used to establish connections among relation algebras, permutation groups, and edge-colored graphs.
TL;DR: In this article, the structural theorem of decomposition of a free differential algebra into a contractible and minimal one is utilised to given an intrinsic definition of the concepts of curvatures and potentials in gauge theories including antisymmetric tensors.
Abstract: The structural theorem of Sullivan of the decomposition of a free differential algebra into a contractible and minimal one is utilised to given an intrinsic definition of the concepts of curvatures and potentials (=connections) in gauge theories including antisymmetric tensors. Applying this idea to d=11 supergravity the author clarifies the role of the 6-index photon showing that all d=11 field equations are a consequence of the principle of rheonomy inserted into the complete differential algebra encompassing both the 3- and 6-forms. Moreover the 6-index photon is dual to the 3-index one as a consequence of the algebra. This is close analogy with the relation between the axion and the dilaton in conformal supergravity. Finally the action of the d=11 theory has a simpler formulation in terms of the curvatures of the full differential algebra.
TL;DR: In this paper, it was shown that exceptional Jordan division algebras arising from the first Tits construction are precisely those where reducing fields and splitting fields agree, and that all isotopes of a first construction exceptional division algebra are isomorphic.
Abstract: In this paper, a certain quadratic form, originally due to Springer [15], which may be associated with any separable cubic subfield living inside an exceptional simple Jordan algebra is related to the coordinate algebra of an appropriate scalar extension. We use this relation to show that, in the presence of the third roots of unity, exceptional Jordan division algebras arising from the first Tits construction are precisely those where reducing fields and splitting fields agree, and that all isotopes of a first construction exceptional division algebra are isomorphic.
TL;DR: In this paper, all possible representations of the BRS algebra in the light of indefinite metric are presented, and all of them are shown to be equivalent to the one presented in this paper.
TL;DR: In this paper, it was shown that a Lie algebra over a field of characteristic 0 with an algebraic adjoint representation is locally finite dimensional, provided the algebra satisfies a polynomial identity.
Abstract: In this paper it is proved that a Lie algebra over a field of characteristic 0 with an algebraic adjoint representation is locally finite dimensional, provided the algebra satisfies a polynomial identity. In particular, a Lie algebra (over a field of characteristic 0) whose adjoint representation is algebraic of bounded degree is locally finite dimensional.Bibliography: 22 titles.
TL;DR: In this paper, the algebra of the upper triangular matrices has been studied for the variety of algebras genelaetu and the main result is that the relatively free algebraic varieties have rational Hilbert (or Poincare) series when the base field is infinite.
Abstract: Subvarieties of the variety of algebras genelaetu by the algebra of the upper triangular matrices are studied in this paper. The main result is that the relatively free algebras have rational Hilbert (or Poincare) series when the base field is infinite. As a corollary, in characteristic 0 the rationality is obtained for varieties not containing the algebra of all 2 × 2 matrices. Some of the results are transfered to Lie and Jordan algebras.
TL;DR: In this paper, the integrals of motion for the Toda lattice were analyzed for two special cases of boundary conditions: the free-end lattice with three non-equal-mass particles and the fixed-ended lattice for two particles.
Abstract: We present new integrals of motion for the Toda lattice (chain of particles in one dimension with exponential interaction) for two special cases of boundary conditions: the free‐end lattice with three non‐equal‐mass particles and the fixed‐end lattice for two particles. In both cases, we use two distinct approaches in order to identify the integrable cases: direct search of the integral of motion and group theoretical methods. Our results are in agreement with the predictions of Painleve analysis.
TL;DR: In this article, it was shown that a finitely generated soluble-by-finite Lie algebra has subexponential growth, which implies that in its universal envelope every subring is an Ore domain.
Abstract: It is proven that a finitely generated soluble-by-finite Lie algebra has a subexponential growth. This implies that in its universal envelope every subring is an Ore domain.
TL;DR: In this paper, it was shown that the quotient algebras with power series generators contain a non-standard ideal, where the ideal is defined as the zero ideal and any other closed ideals are denoted nonstandard ideals.
Abstract: and, of course, the zero ideal. Such ideals are referred to as standard ideals. Any other closed ideals are denoted nonstandard ideals. It has been an open question for some time whether there exists any algebra weight {w(n)} such that ^(^(n)) contains a nonstandard ideal [6, p. 189], and the problem seems to go back to Silov (a proposed solution appearing in the literature [6, p. 205] is in error). Interest has also been focused upon the quotient algebras (^(i^n))//), where / is assumed to be nonstandard, since these algebras are representative of all radical Banach algebras with power series generators [1]. Our result is the following:
TL;DR: In this article, it was shown that the variety generated by Murskii's algebra contains uncountably many subvarieties, and that it is possible to construct a variety with many subvariants.
Abstract: It is shown that the variety generated by Murskii's algebra contains uncountably many subvarieties.