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The cotangent cohomology of {\it S. Lichtenbaum} and {\it M. Schlessinger} [Trans. Am. Math. Soc. 128, 41-70 (1967; Zbl 0156.27201)]\ is known for its ability to control the deformation of the structure of a commutative algebra. \par Considering algebras in the wider sense to include coalgebras, bialgebras and similar algebraic structures such as the Drinfel'd algebras encountered in the theory of quantum groups, one can model such objects as models for an algebraic theory much in the sense of {\it F. W. Lawvere} [Proc. Natl. Acad. Sci. USA 50, 869-872 (1963)]. Individual algebras are then determined by their structural constants and hence may be amenable to a deformation theoretic approach for determining their stability under change of these constants. \par The basic notion of presentation of an algebraic theory allows the author to develop a deformation cohomology theory, based on the type of construction initially used by Lichtenbaum and Schlessinger, and to s! (English) |
