A brief introduction to pre
... Classical and quantum Yang-Baxter equations: Svinolupov and Sokolov(1994), Etingof and Soloviev(1999), Golubschik and Sokolov(2000), · · · Poisson brackets and infinite-dimensional Lie algebras: Gel’fand and Dorfman(1979), Dubrovin and Novikov(1984), Balinskii and Novikov(1985), · · · Quantum field ...
... Classical and quantum Yang-Baxter equations: Svinolupov and Sokolov(1994), Etingof and Soloviev(1999), Golubschik and Sokolov(2000), · · · Poisson brackets and infinite-dimensional Lie algebras: Gel’fand and Dorfman(1979), Dubrovin and Novikov(1984), Balinskii and Novikov(1985), · · · Quantum field ...
CONVERGENCE THEOREMS FOR PSEUDO
... Example 4.6. LetQI = [0, 1], an uncountable index set and let RI denote the Cartesian product i∈I Ri (without topology), where for all i, Ri = R. Now let RI be endowed with the product topology τ and consider E := (RI , τ ) as an algebra, with jointly continuous multiplication defined pointwise. The ...
... Example 4.6. LetQI = [0, 1], an uncountable index set and let RI denote the Cartesian product i∈I Ri (without topology), where for all i, Ri = R. Now let RI be endowed with the product topology τ and consider E := (RI , τ ) as an algebra, with jointly continuous multiplication defined pointwise. The ...
Cohomology as the derived functor of derivations.
... has a left adjoint; i.e. there is a functor E: <&0-+'é and an isomorphism of bifunctors <^0(—, —) = '^(F(-), —), where r€(T,R) denotes morphisms from T to R in '€. In Cases A and S, F(U) is the tensor algebra on U; in Case L the free Lie algebra on U, defined as the appropriate homomorphic image of ...
... has a left adjoint; i.e. there is a functor E: <&0-+'é and an isomorphism of bifunctors <^0(—, —) = '^(F(-), —), where r€(T,R) denotes morphisms from T to R in '€. In Cases A and S, F(U) is the tensor algebra on U; in Case L the free Lie algebra on U, defined as the appropriate homomorphic image of ...
DEFORMATION THEORY
... 5. dg-Lie algebras and the Maurer-Cartan equation 6. L∞ -algebras and the Maurer-Cartan equation 7. Homotopy invariance of the Maurer-Cartan equation 8. Deformation quantization of Poisson manifolds Conventions. All algebraic objects will be considered over a fixed field k of characteristic zero. Th ...
... 5. dg-Lie algebras and the Maurer-Cartan equation 6. L∞ -algebras and the Maurer-Cartan equation 7. Homotopy invariance of the Maurer-Cartan equation 8. Deformation quantization of Poisson manifolds Conventions. All algebraic objects will be considered over a fixed field k of characteristic zero. Th ...
Reasoning in Algebra
... Reasoning in Algebra Objectives: 1) To develop an awareness of the structure of a mathematical system, connecting postulates, logical reasoning, and theorems. 2) To connect reasoning in algebra and geometry. Properties of Equality ...
... Reasoning in Algebra Objectives: 1) To develop an awareness of the structure of a mathematical system, connecting postulates, logical reasoning, and theorems. 2) To connect reasoning in algebra and geometry. Properties of Equality ...
Hochschild cohomology: some methods for computations
... Lemma 2.5 The Ae –module A is projective if and only if there exists an element e ∈ Ae such that µ(e) = 1 and ae = ea, for any a in A. Proof: Assume that A is Ae –projective. Then the Ae –epimorphism ...
... Lemma 2.5 The Ae –module A is projective if and only if there exists an element e ∈ Ae such that µ(e) = 1 and ae = ea, for any a in A. Proof: Assume that A is Ae –projective. Then the Ae –epimorphism ...
skew-primitive elements of quantum groups and braided lie algebras
... Yetter-Drinfel'd modules form a category YD in the obvious way (morphisms are the K -module homomorphisms which are also K -comodule homomorphisms). The most interesting structure on YD is given by its tensor products. It is well known that the tensor product M N of two vector spaces which are K - ...
... Yetter-Drinfel'd modules form a category YD in the obvious way (morphisms are the K -module homomorphisms which are also K -comodule homomorphisms). The most interesting structure on YD is given by its tensor products. It is well known that the tensor product M N of two vector spaces which are K - ...
An explicit example of a noncrossed product division algebra
... There is a result6 that limits the hope of finding an explicit noncrossed product example of the form D(x, σ) : If D is a quaternion algebra over a local or global field then any D(x, σ) is a crossed product. With this result in mind, it is clear that even though we do not achieve the smallest possi ...
... There is a result6 that limits the hope of finding an explicit noncrossed product example of the form D(x, σ) : If D is a quaternion algebra over a local or global field then any D(x, σ) is a crossed product. With this result in mind, it is clear that even though we do not achieve the smallest possi ...