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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Czechoslovak journal of physics 46 (1996), S. 1227-1233 
    ISSN: 1572-9486
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present some results concerning the generalized homologies associated with nilpotent endomorphismsd such thatd N =0 for some integerN≥2. We then introduce the notion of gradedq-differential algebra and describe some examples. In particular we construct theq-analog of the simplicial differential on forms, theq-analog of the Hochschild differential and theq-analog of the universal differential envelope of an associative unital algebra.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    K-Theory 14 (1998), S. 371-404 
    ISSN: 1573-0514
    Keywords: Homology ; N-complexes ; simplicial modules ; Hochschild homology ; 9-calculu
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the generalized homology associated with a nilpotent endomorphism d satisfying d N = 0,For simplicial modules, we construct such nilpotent endomorphisms and we prove a general result relating the corresponding generalized homologies to the ordinary homology. We also discuss the generalization of the notion of graded differential algebra in this context.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 37 (1996), S. 467-474 
    ISSN: 1573-0530
    Keywords: 16D20 ; Noncommutative differential geometry ; bimodules ; differential operators ; symbols ; connections
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We analyse the structure of the first-order operators in bimodules introduced by A. Connes. We apply this analysis to the theory of connections on bimodules, thereby generalizing several proposals.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 42 (1997), S. 183-192 
    ISSN: 1573-0530
    Keywords: WZNW model ; generalized cohomologies.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The zero modes of the monodromy extended SU(2) WZNW model give rise to a gauge theory with a finite-dimensional state space. A generalized BRS operator A such that $$A^h = 0\left( {h = k + 2 = 3,4,...} \right.$$ being the height of the current algebra representation) acts in $$\left( {2h - 1} \right)$$ -dimensional indefinite metric space $${\mathcal{H}}_I$$ of quantum group invariant vectors. The generalized cohomologies Ker $$A^n /{Im}\;A^{h - n} \left( {n = 1,...,h - 1} \right)$$ are 1-dimensional. Their direct sum spans the physical subquotient of $${\mathcal{H}}_I$$ .
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 48 (1999), S. 323-338 
    ISSN: 1573-0530
    Keywords: WZNW model ; generalized homology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We generalize the BRS method for the (finite-dimensional) quantum gauge theory involved in the zero modes of the monodromy extended SU(2) WZNW model. The generalization consists of a nilpotent operator Q such that Qh = 0 (h = k + 2 = 2, 3, ... being the height of the current algebra representation) acting on an extended state space. The physical subquotient is identified with the direct sum ⊕ h-1 n=1 Ker(Qn)/Im(Qh−n).
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 19 (1990), S. 121-126 
    ISSN: 1573-0530
    Keywords: 16A24 ; 20Gxx ; 42A38 ; 81Cxx
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract By using the results of S. L. Woronowicz, we show that for the twisted version of the classical compact matrix groups, the Hopf algebraA h of representative elements is isomorphic as a co-algebra to the Hopf algebraA O of representative functions on the classical group. As a consequence,A h can be identified withA O as a co-algebra but with an associative product, called the star-product, which is a deformation of the original commutative product ofA O . Furthermore, the construction of this star product from the original product is connected to the Fourier transformation in a manner which is similar to the construction of quantum mechanics from classical mechanics on phase space. In fact, we shall describe the analog of the Weyl correspondence.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 49 (1999), S. 245-252 
    ISSN: 1573-0530
    Keywords: N-complexes ; Young diagrams ; irreducible tensors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We construct N-complexes of noncompletely antisymmetric irreducible tensor fields on ℝ D , thereby generalizing the usual complex (N=2) of differential forms. These complexes arise naturally in the description of higher spin gauge fields. Although, for N ⩾ 3, the generalized cohomology of these N-complexes is nontrivial, we give a generalization of the Poincaré lemma. Several results which have appeared in various contexts are shown to be particular cases of this generalized Poincaré lemma.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 316-322 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The noncommutative differential geometry of the algebra Mn (C) of complex n×n matrices is investigated. The role of the algebra of differential forms is played by the graded differential algebra C(sl(n,C),Mn (C))=Mn (C)⊗Λsl(n,C)*,sl(n,C) acting by inner derivations on Mn (C). A canonical symplectic structure is exhibited for Mn (C) for which the Poisson bracket is, to within a factor i, the commutator. Also, a canonical Riemannian structure is described for Mn (C). Finally, the analog of the Maxwell potential is constructed and it is pointed out that there is a potential with a vanishing curvature that is not a pure gauge.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 213-223 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show that expressed in the appropriate principal bundles, the gravitational and Yang-Mills fields equations are equivalent to integrability conditions and that the latter can also be interpreted, using local sections, as conservation equations of the local pseudo-densities of energy-momentum and Yang-Mills charge respectively. These densities can be related using a Kaluza-Klein unification.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 43 (1975), S. 225-254 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A (non-commutative) generalization of the classical moment problem is formulated on arbitrary *-algebras with units. This is used to produce aC*-algebra associated with the space of test functions for quantum fields. ThisC*-algebra plays a role in theories of bounded localized observables in Hilbert space which is similar to that of the space of test functions in quantum field theories (namely it is represented in Hilbert space). The case of local quantum fields which satisfy a slight generalization of the growth condition is investigated.
    Type of Medium: Electronic Resource
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