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Operator algebra
About: Operator algebra is a research topic. Over the lifetime, 5783 publications have been published within this topic receiving 165303 citations.
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TL;DR: In this paper, the four-dimensional Green-Schwarz superstring is quantized in a manifestly SO(3,1) super-Poincare covariant manner.
152 citations
TL;DR: In this paper, it was shown that the spectral problem for Yang's system is related to the problem of finding the spherical tempered representations of the graded Hecke algebra, which is a simple realization of a certain algebra of operators acting on a space of smooth functions.
Abstract: The graded Hecke algebra has a simple realization as a certain algebra of operators acting on a space of smooth functions. This operator algebra arises from the study of the root system analogue of Yang's system of n particles on the real line with delta function potential. It turns out that the spectral problem for this generalization of Yang's system is related to the problem of finding the spherical tempered representations of the graded Hecke algebra. This observation turns out to be very useful for both these problems. Application of our technique to affine Hecke algebras yields a simple formula for the formal degree of the generic Iwahori spherical discrete series representations.
151 citations
Book•
31 Dec 1987
TL;DR: In this paper, the general scheme in matrix rings and N-Soliton solutions of nonlinear equations is realized in operator algebra. But it is not a generalization of the generalized derivation and logarithmic derivative.
Abstract: 1. General Scheme.- 1 Generalized Derivation and Logarithmic Derivatives.- 2 Examples of Nonlinear Equations.- 3 Projection Operation.- 2. Realization of the General Scheme in Matrix Rings and N-Soliton Solutions.- 1 Wronsky Matrices.- 2 Conditions of Invertibility of Some Wronsky Matrices.- 3 N-Soliton Solutions of Nonlinear Equations.- 4 Singular Solutions of Nonlinear Equations.- 3. Realization of the General Scheme in Operator Algebras.- 1 Extenstion of Algebra C?(B(H0).- 2 Solving Linear Equations in Algebra C?(B(H)).- 3 Additional Equations.- 4 Choice of Parameters.- 5 Properties of Logarithmic Derivatives with Respect to Conjunction Operation.- 6 Invertibility Conditions for Operators $$ \hat{\Gamma } $$.- 4. Classes of Solutions to Nonlinear Equations.- 1 Examples of Solutions to Nonlinear Equations.- 2 Connection with Inverse Problems of Spectral Analysis.- 3 KP Equation.- References.
151 citations
Journal Article•
TL;DR: In this article, the authors investigated whether the topology from this metric coincides with the weak-* topology (our definition of a compact quantum metric space) and gave an affirmative answer for G = Z d when l is a word-length, or the restriction to Z d of a norm on R d.
Abstract: Let l be a length function on a group G, and let M l denote the operator of pointwise multiplication by l on l 2 (G). Following Connes, M l can be used as a Dirac operator for C* r (G). It defines a Lipschitz seminorm on C* r (G), which defines a metric on the state space of C* r (G). We investigate whether the topology from this metric coincides with the weak-* topology (our definition of a compact quantum metric space). We give an affirmative answer for G = Z d when l is a word-length, or the restriction to Z d of a norm on R d . This works for C* r (G) twisted by a 2-cocycle, and thus for non-commutative tori. Our approach involves Connes' cosphere algebra, and an interesting compactification of metric spaces which is closely related to geodesic rays.
151 citations
TL;DR: In this article, a supersymmetric Faddeev-Popov ghost sector was added to the Bagger-Lambert theory based on a Lorentzian three algebra.
Abstract: We show that by adding a supersymmetric Faddeev-Popov ghost sector to the recently constructed Bagger-Lambert theory based on a Lorentzian three algebra, we obtain an action with a BRST symmetry that can be used to demonstrate the absence of negative norm states in the physical Hilbert space. We show that the combined theory, expanded about its trivial vacuum, is BRST equivalent to a trivial theory, while the theory with a vev for one of the scalars associated with a null direction in the three-algebra is equivalent to a reformulation of maximally supersymmetric 2+1 dimensional Yang-Mills theory in which there is a formal SO(8) superconformal invariance.
150 citations