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NONCOMMUTATIVE POISSON STRUCTURES, DERIVED REPRESENTATION SCHEMES AND CALABIYAU ALGEBRAS
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Derived Representation Schemes and Noncommutative Geometry
, 2011
"... After surveying relevant literature (on representation schemes, homotopical algebra, and noncommutative algebraic geometry), we provide a simple algebraic construction of relative derived representation schemes and prove that it constitutes a derived functor in the sense of Quillen. Using this co ..."
Abstract

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After surveying relevant literature (on representation schemes, homotopical algebra, and noncommutative algebraic geometry), we provide a simple algebraic construction of relative derived representation schemes and prove that it constitutes a derived functor in the sense of Quillen. Using this construction, we introduce a derived KontsevichRosenberg principle. In particular, we construct a (nonabelian) derived functor of a functor introduced by Van den Bergh that offers one (particularly significant) realization of the principle. We also prove a theorem allowing one to finitely present derived representation schemes of an associative algebra whenever one has an explicit finite presentation for an almost free resolution of that algebra; using this theorem, we calculate several examples (including some computer calculations of homology). BIOGRAPHICAL SKETCH George Khachatryan was born in Moscow, Russia on December 5, 1984, and moved to the United States with his family in 1990. After graduating from the Kinkaid School in 2003, he attended the University of Chicago. From 2007 to
Contemporary Mathematics Derived Representation Schemes and Noncommutative Geometry
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