Mathematical Sciences: Noncommutative Algebras

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This research is concerned with the structure of certain noncommutative algebras. The main concern is the structure of algebras which arise as deformations of fixed rings of the Weyl algebras. The techniques used to study these algebras involve the intertwining of ideas from the theory of Lie algebras and algebraic geometry. The principle investigator will also pursue the study of enveloping algebras, focusing on the problem of calculating the K-theory of primitive factors of the enveloping algebra of a semi-simple Lie algebra. Noncommutative ring theory represents the study of an algebraic structure possessing an addition and a noncommutative multiplication. K-theory represents the evolved algebraic theory of vector spaces and linear mappings. This project is concerned with the structure, K-theory and state-space of certain noncommutative rings.