Geometry of noncommutative algebras
نویسندگان
چکیده
منابع مشابه
Hopf Algebras in Noncommutative Geometry
We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic coh...
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A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the h-deformed plane and the quantum group GLp,q(2) are recovered in this way. Geometric structures like metrics and compatible linear connections are introduced.
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Elements of noncommutative differential geometry of Z-graded generalized Weyl algebras A(p; q) over the ring of polynomials in two variables and their zero-degree subalgebras B(p; q), which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed. In particular, three classes of skew derivations of A(p; q) are constructed, and three-dimensional first-...
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Recently, V. Ginzburg proved that Calogero phase space is a coadjoint orbit for some infinite dimensional Lie algebra coming from noncommutative symplectic geometry, [12]. In this note we generalize his argument to specific quotient varieties of representations of (deformed) preprojective algebras. This result was also obtained independently by V. Ginzburg [13]. Using results of W. Crawley-Boev...
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 2011
ISSN: 0137-6934,1730-6299
DOI: 10.4064/bc93-0-6