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The infinitesimal algebraic object associated with a Lie groupoid. A Lie algebroid over a manifold B is a vector bundle A over B with a Lie algebra structure [,] (Lie ...

There are two types of singular values, one in the context of elliptic integrals, and the other in linear algebra. For a square matrix A, the square roots of the eigenvalues ...

A finite-dimensional Lie algebra all of whose elements are ad-nilpotent is itself a nilpotent Lie algebra.

If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers.

A generalization of a Heyting algebra which replaces Boolean algebra in "intuitionistic" logic.

An algebra which does not satisfy a(bc)=(ab)c is called a nonassociative algebra.

A representation of a C^*-algebra A is a pair (H,phi) where H is a Hilbert space and phi:A->B(H) is a *-homomorphism. (H,phi) is said to be faithful if phi is injective. For ...

A set equipped with a sigma-algebra of subsets.

An operator A^~ such that A^~^2=A^~ or an element of an algebra x such that x^2=x.

A set considered together with the sigma-algebra on the set.