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The word "algebra" is a distortion of the Arabic title of a treatise by al-Khwārizmī about algebraic methods. In modern usage, algebra has several meanings. One use of the ...

Kontsevich's integral is a far-reaching generalization of the Gauss integral for the linking number, and provides a tool to construct the universal Vassiliev invariant of a ...

Every finite-dimensional Lie algebra of characteristic p=0 has a faithful finite-dimensional representation.

Let G=SL(n,C). If lambda in Z^n is the highest weight of an irreducible holomorphic representation V of G, (i.e., lambda is a dominant integral weight), then the G-map ...

An operator Gamma=sum_(i=1)^me_i^Ru^(iR) on a representation R of a Lie algebra.

Let A be any algebra over a field F, and define a derivation of A as a linear operator D on A satisfying (xy)D=(xD)y+x(yD) for all x,y in A. Then the set D(A) of all ...

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

Every finite-dimensional Lie algebra of characteristic p!=0 has a faithful finite-dimensional representation.

A simple root of a Lie algebra is a positive root that is not the sum of two positive roots.

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 ...