Etymology From nil (“not any”) + potent (“having power”) with literal meaning “having zero power” - bearing Latin roots nil and potens. Coined in 1870, along with idempotent, by American mathematician Benjamin Peirce to describe elements of associative algebras.
Algebra, Mathematics, Sciences Such that, for some positive integer n, xⁿ = 0.
Of an element x of a ring
If a square matrix is upper triangular and has zeros on the diagonal, then it is nilpotent (under the usual matrix multiplication).
The rest of this book is devoted to determining the conjugacy classes and centralizers of nilpotent elements in L(G) and unipotent elements in G, where G is an exceptional algebraic group of type E₈,E₇, E₆, F₄ or G₂ over an algebraically closed field K of characteristic p. This chapter contains statements of the main results for nilpotent elements.2012, Martin W. Liebeck, Gary M. Seitz, Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras, American Mathematical Society, page 129:
› In any of several technical senses: behaving…
2
Algebra, Mathematics, Sciences Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
Of an element x of a Lie algebra L
3
Algebra, Mathematics, SciencesOf a Lie algebra Such that the lower central series terminates.
Algebra, Mathematics, SciencesOf an ideal I Such that there exists a natural number k with Iᵏ = 0.
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Algebra, Mathematics, SciencesOf a semigroup with zero Containing only nilpotent elements.
Semigroup theory
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Algebra, Mathematics, Sciences Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
Etymology From nil (“not any”) + potent (“having power”) with literal meaning “having zero power” - bearing Latin roots nil and potens. Coined in 1870, along with idempotent, by American mathematician Benjamin Peirce to describe elements of associative algebras.
The so-called spinor algebra of C(2), the language of the quantum mechanics, is formulated in terms of the idempotents and nilpotents of the geometric algebra of space, including its beautiful representation on the Riemann sphere, and a new proof of the Heisenberg uncertainty principle.2015, Garret Sobczyk, “Part I: Vector Analysis of Spinors”, in arXiv: