Homological Dimensions of the Gelfand-Shilov Algebras

Student: Fedorov Igor

Educational Programme: Mathematics (Master)

Final Grade: 10

Year of Graduation: 2020

The function spaces K{M_p}, introduced by I. M. Gelfand and G. E. Shilov in 1960s, form a general class of spaces of test functions for the theory of distributions. This class includes, for example, the Schwartz space of rapidly decreasing functions. These spaces are topological algebras with respect to pointwise multiplication of functions. We compute the global dimensions for some general class of these algebras, using the variant of homological theory developed by A. Ya. Helemskii and J. Taylor for the needs of functional analysis. It turns out that for algebras in our class the global dimension is equal to the dimension of the domain of definition (that is to say, it is m for algebras of functions on R^m).

Full text (added June 1, 2020)

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