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A band over a fixed topological space X is represented by a cover X= union U_alpha, U_alpha subset= X, and for each alpha, a sheaf of groups K_alpha on U_alpha along with ...

There are no fewer than two closely related but somewhat different notions of gerbe in mathematics. For a fixed topological space X, a gerbe on X can refer to a stack of ...

A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

"The" I graph is the path graph on two vertices: P_2. An I-graph I(n,j,k) for 1<=j,k<n and j,k!=n/2 is a generalization of a generalized Petersen graph and has vertex set ...

Let K be a field, and A a K-algebra. Elements y_1, ..., y_n are algebraically independent over K if the natural surjection K[Y_1,...,Y_n]->K[y_1,...,y_n] is an isomorphism. ...

An automorphism is an isomorphism of a system of objects onto itself. The term derives from the Greek prefix alphaupsilontauomicron (auto) "self" and ...

The word canonical is used to indicate a particular choice from of a number of possible conventions. This convention allows a mathematical object or class of objects to be ...

Each Cartan matrix determines a unique semisimple complex Lie algebra via the Chevalley-Serre, sometimes called simply the "Serre relations." That is, if (A_(ij)) is a k×k ...

A coequalizer of a pair of maps f,g:X->Y in a category is a map c:Y->C such that 1. c degreesf=c degreesg, where degrees denotes composition. 2. For any other map c^':Y->C^' ...

There are at least two meanings on the word congruent in mathematics. Two geometric figures are said to be congruent if one can be transformed into the other by an isometry ...