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Functional analysis and its applications
December 22, 2016 10:30–11:50
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Flow of finite-dimensional algebras
U. A. Rozikov Institute of Ìathematics, National University of Uzbekistan
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Abstract:
We introduce the notion of flow (depending on time) of finite-dimensional algebras (FA). This flow can be considered as a particular case of (continuous-time) dynamical system whose states are finite-dimensional algebras with matrices of structural constants satisfying an analogue of Kolmogorov-Chapman equation. We define stochastic FA generated by known quadratic stochastic processes and give a construction of an FA which contains algebras of arbitrary (finite) dimension. We discuss the time depending behavior (dynamics) of the properties in FA.
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