connecting homomorphism

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• Bockstein homomorphism — In mathematics, the Bockstein homomorphism in homological algebra is a connecting homomorphism associated with a short exact sequence:0 → P → Q → R → 0of abelian groups, when they are introduced as coefficients into a chain complex C , and which… …   Wikipedia

• Clifford algebra — In mathematics, Clifford algebras are a type of associative algebra. They can be thought of as one of the possible generalizations of the complex numbers and quaternions.[1][2] The theory of Clifford algebras is intimately connected with the… …   Wikipedia

• Orthogonal group — Group theory Group theory …   Wikipedia

• Homological algebra — is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract… …   Wikipedia

• Snake lemma — The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences. The snake lemma is valid in every abelian category and is a crucial tool in homological algebra and its applications, for instance …   Wikipedia

• Cotangent complex — In mathematics the cotangent complex is a roughly a universal linearization of a morphism of geometric or algebraic objects. Cotangent complexes were originally defined in special cases by a number of authors. Luc Illusie, Daniel Quillen, and M.… …   Wikipedia

• Spectral sequence — In the area of mathematics known as homological algebra, especially in algebraic topology and group cohomology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a… …   Wikipedia

• Galois cohomology — In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups. A Galois group G associated to a field extension L / K acts in a natural way… …   Wikipedia

• Severi-Brauer variety — In mathematics, a Severi Brauer variety over a field K is an algebraic variety V which becomes isomorphic to projective space over an algebraic closure of K . Examples are conic sections C : provided C is non singular, it becomes isomorphic to… …   Wikipedia

• Approximately finite dimensional C*-algebra — In C* algebras, an approximately finite dimensional, or AF, C* algebra is one that is the inductive limit of a sequence of finite dimensional C* algebras. Approximate finite dimensionality was first defined and described combinatorially by… …   Wikipedia

• Covering space — A covering map satisfies the local triviality condition. Intuitively, such maps locally project a stack of pancakes above an open region, U, onto U. In mathematics, more specifically algebraic topology, a covering map is a continuous surjective… …   Wikipedia