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1.
We investigate the propeties of differential algebras generated by an operator d satisfying the property dN = 0 instead of d2 = 0 as in the usual case. Several examples of realizations of such differential algebras are given, either in the context of ZN-graded N × N matrix algebras, or as a generalized differential calculus on manifolds. 相似文献
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We propose a theoretical classification of one-dimensional deterministic cellular automata in two types, typeS and typeO. This classification is connected with the phenomenological classification of S. Wolfram. 相似文献
4.
Michel Dubois-Violette 《Communications in Mathematical Physics》1975,43(3):225-254
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.
Laboratorie associé au Centre National de la Recherche Scientifique. 相似文献
5.
This paper contains detailed proofs of our results on the moduli space and the structure of noncommutative 3-spheres. We develop
the notion of central quadratic form for quadratic algebras, and a general theory which creates a bridge between noncommutative
differential geometry and its purely algebraic counterpart. It allows to construct a morphism from an involutive quadratic
algebra to a C*-algebra constructed from the characteristic variety and the hermitian line bundle associated to the central
quadratic form. We apply the general theory in the case of noncommutative 3-spheres and show that the above morphism corresponds
to a natural ramified covering by a noncommutative 3-dimensional nilmanifold. We then compute the Jacobian of the ramified
covering and obtain the answer as the product of a period (of an elliptic integral) by a rational function. We describe the
real and complex moduli spaces of noncommutative 3-spheres, relate the real one to root systems and the complex one to the
orbits of a birational cubic automorphism of three dimensional projective space. We classify the algebras and establish duality
relations between them. 相似文献
6.
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
being the height of the current algebra representation) acts in
-dimensional indefinite metric space
of quantum group invariant vectors. The generalized cohomologies Ker
are 1-dimensional. Their direct sum spans the physical subquotient of
. 相似文献
7.
We generalize the notion, introduced by Henri Cartan, of an operation of a Lie algebra ${\mathfrak{g}}$ in a graded differential algebra Ω. We define the notion of an operation of a Hopf algebra ${\mathcal{H}}$ in a graded differential algebra Ω which is referred to as a ${\mathcal{H}}$ -operation. We then generalize for such an operation the notion of algebraic connection. Finally we discuss the corresponding noncommutative version of the Weil algebra: The Weil algebra ${W(\mathcal{H})}$ of the Hopf algebra ${\mathcal{H}}$ is the universal initial object of the category of ${\mathcal{H}}$ -operations with connections. 相似文献
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We exhibit large classes of local actions for the vacuum Einstein equations. In presence of fermions, or more generally of
matter which couple to the connection, these actions lead to inequivalent equations revealing an arbitrary number of parameters.
Even in the pure gravitational sector, any corresponding quantum theory would depend on these parameters. 相似文献
10.
M. Dubois-Violette J. Madore T. Masson J. Mourad 《Letters in Mathematical Physics》1995,35(4):351-358
A general definition has been proposed recently of a linear connection and a metric in noncommutative geometry. It is shown that to within normalization there is a unique linear connection on the quantum plane and there is no metric. 相似文献