NONCOMMUTATIVE STRUCTURES IN MATHEMATICS AND PHYSICS

By MARK ANDERSON

GAUGE THEORIES BEYOND GAUGE THEORY SYMMETRIES WIDER THAN SUPERSYMMETRY TENSIONS IN SUPERGRAVITY BRANEWORLDS AN UNCONVENTIONAL SUPERGRAVITY SUPERSYMMETRY OF RS BULK AND BRANE D-BRANES AND VACUUM PERIODICITY QUANTUM DEFORMATIONS OF SPACE-TIME SUSY AND NONCOMMUTATIVE SUPERFIELD THEORY THE HOWE DUALITY AND LIE SUPERALGEBRAS ENVELOPING ALGEBRA OF GL(3) AND ORTHOGONAL POLYNOMIALS NONINVERTIBILITY, SEMISUPERMANIFOLDS AND CATEGORIES REGULARIZATION AN OVERVIEW OF NEW SUPERSYMMETRIC GAUGE THEORIES WITH 2-FORM GAUGE POTENTIALS CONTENTS SUPERSYMMETRIC R4 ACTIONS AND QUANTUM CORRECTIONS TO SUPERSPACE TORSION CONSTRAINTS MASSIVE SUPERPARTICLE WITH SPINORIAL CENTRAL CHARGES ROTATING SUPER BLACK HOLE AS SPINNING PARTICLE CLASSIFYING N-EXTENDED 1-DIMENSIONAL SUPER SYSTEMS PARA, PSEUDO, AND ORTHOSUPERSYMMETRIC QUANTUM MECHANICS AND THEIR BOSONIZATION SUPERSYMMETRIC ODD MECHANICAL SYSTEMS AND HILBERT Q-MODULE QUANTIZATION LOCALLY ANISOTROPIC SUPERGRAVITY AND GAUGE GRAVITY ON NONCOMMUTATIVE SPACES FINITENESS IN CONVENTIONAL N = 1 GUTS WORLD VOLUME REALIZATION OF AUTOMORPHISMS SOME METRICS ON THE MANIN PLANE COHERENCE ISOMORPHISMS FOR A HOPF CATEGORY FUSION RINGS AND TENSOR CATEGORIES ON CATEGORIES OF GELFAND-ZETLIN MODULES HIDDEN SYMMETRY OF SOME ALGEBRAS OF Q-DIFFERENTIAL OPERATORS A FAMILY OF *-ALGEBRAS ALLOWING WICK ORDERING: FOCK REPRESENTATIONS AND UNIVERSAL ENVELOPING C*-ALGEBRAS NONSTANDARD QUANTIZATION OF THE ENEVLOPING ALGEBRA U(SO(N)) AND ITS APPLICATIONS CAN THE CABIBBO MIXING ORIGINATE FROM NONCOMMUTATIVE EXTRA DIMENSIONS? NONCLASSICAL TYPE REPRESENTATIONS OF NONSTANDARD QUANTIZATION OF ENVELOPING ALGEBRAS U(SO(N)), U(SO(N,1)) AND U(ISO(N)) QUASIPARTICLES IN NON-COMMUTATIVE FIELD THEORY TIME DEPENDENCE AND (NON)COMMUTATIVITY OF SYMMETRIES OF EVOLUTION EQUATIONS P-ADIC STRINGS AND NONCOMMUTATIVITY ADELIC QUANTUM MECHANICS: NONARCHIMEDEAN AND NONCOMMUTATIVE ASPECTS GIBBS STATES OF A LATTICE SYSTEM OF QUANTUM ANHARMONIC OSCILLATORS A METRIC-AFFINE FIELD MODEL FOR THE NEUTRINO GENERALIZED TAUB-NUT METRICS AND KILLING-YANO TENSORS AN EFFECTIVE MODEL OF THE SPACETIME FOAM POSSIBLE CONSTRAINTS ON STRING THEORY IN CLOSED SPACE WITH SYMMETRIES