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On a Lie group, exp is a map from the Lie algebra to its Lie group. If you think of the Lie algebra as the tangent space to the identity of the Lie group, exp(v) is defined ...

The number of nonassociative n-products with k elements preceding the rightmost left parameter is F(n,k) = F(n-1,k)+F(n-1,k-1) (1) = (n+k-2; k)-(n+k-1; k-1), (2) where (n; k) ...

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 ...

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 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.