Deformations of Associative Algebras with Inner Products
نویسندگان
چکیده
We develop the deformation theory of A∞ algebras together with∞-inner products and identify a differential graded Lie algebra that controls the theory. This generalizes the deformation theories of associative algebras, A∞ algebras, associative algebras with inner products, and A∞ algebras with inner products.
منابع مشابه
Massey Products and Deformations
It is common knowledge that the construction of one-parameter deformations of various algebraic structures, like associative algebras or Lie algebras, involves certain conditions on cohomology classes, and that these conditions are usually expressed in terms of Massey products, or rather Massey powers. The cohomology classes considered are those of certain differential graded Lie algebras (DGLA...
متن کاملQuantum deformations of associative algebras and integrable systems
Quantum deformations of the structure constants for a class of associative noncommutative algebras are studied. It is shown that these deformations are governed by the quantum central systems which has a geometrical meaning of vanishing Riemann curvature tensor for Christoffel symbols identified with the structure constants. A subclass of isoassociative quantum deformations is described by the ...
متن کاملValued deformations of algebras
We develop the notion of deformations using a valuation ring as ring of coefficients. This permits to consider in particular the classical Gerstenhaber deformations of associative or Lie algebras as infinitesimal deformations and to solve the equation of deformations in a polynomial frame. We consider also the deformations of the enveloping algebra of a rigid Lie algebra and we define valued de...
متن کاملar X iv : 0 81 1 . 47 25 v 2 [ m at h . R A ] 1 2 M ay 2 00 9 On the deformation theory of structure constants for associative algebras
Algebraic scheme for constructing deformations of structure constants for associative algebras generated by a deformation driving algebras (DDAs) is discussed. An ideal of left divisors of zero plays a central role in this construction. Deformations of associative three-dimensional algebras with the DDA being a three-dimensional Lie algebra and their connection with integrable systems are studied.
متن کامل2 8 N ov 2 00 8 On the deformation theory of structure constants for associative algebras
Algebraic scheme for constructing deformations of structure constants for associative algebras generated by a deformation driving algebras (DDAs) is proposed. An ideal of left divisors of zero plays a central role in this construction. Deformations of associative commutative three-dimensional algebras with the DDA being a three-dimensional Lie algebra and their connection with integrable system...
متن کامل