Trivial Construction of Free Associative Conformal Algebra
نویسنده
چکیده
Theory of conformal algebras (see [K1], [K2], [K3]) is a relatively new branch of algebra closely related to mathematical physics. The general categorial approach in this theory leads to the notion of pseudotensor category [BD] (also known as multicategory [La]). Algebras in these categories (so called pseudoalgebras, see [BDK]) allow to get a common presentation of various features of usual and conformal algebras. Free associative, commutative and Lie conformal algebras were investigated in [Ro1], [Ro2] by using their coefficient algebras. There were found the bases of free associative conformal algebra and its coefficient algebra (positive component). Another construction of free associative conformal algebra was given in [BFK], where it was built without using coefficient algebra. In this paper, we adduce another (and quite short) construction of free associative conformal algebra and discuss some possibilities of applying some analogous constructions in the theory of conformal algebras. This work was supported by RFBR, project 01–01–00630. Author is very grateful to L. A. Bokut, I. V. L’vov, V. N. Zhelyabin and E. I. Zel’manov for their interest to this work and helpful discussions.
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