nilpotent


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nilpotent

[¦nil′pōt·ənt]
(mathematics)
An element of some algebraic system which vanishes when raised to a certain power.
References in periodicals archive ?
As g is nilpotent, elements in G have inverses given by
1] be the m x m nilpotent matrix which is zero everywhere except for ones along the first superdiagonal.
n] is nilpotent if and only if A has only the eigenvalue [lambda], it follows that [R.
In [7] the author described all the Frobenius algebraic Lie algebras G = R+N whose nilpotent radical N is Abelian in the following two cases: the reductive Levi subalgebra R acts on N irreducibly; R is simple.
r] is nilpotent with the index of nilpotency v that is equal to the index of the pencil [lambda]E - A.
Nilpotent preservers were discussed by Song, Kang and Jun [13] and Li and Tan [5].
Background information on invariant theory, algebraic geometry, central simple algebras, and the representation theory of quivers is given, followed by chapters on the main results of Cayley-smooth orders, semisimple representations, nilpotent representations, noncommutative manifolds, and moduli spaces.
Among the topics are Dirac cohomology and nilpotent representations of complex groups, the Witt construction in characteristics one and quantization, the analogy between complex semisimple groups and their Cartan motion groups, a super version of Connes-Moscovici Hopf algebra, two exact sequences for lattice cohomology, and large scale geometry and its applications.
Their topics include moduli spaces of twisted sheaves on a projective variety, integral Hodge classes on uni-ruled or Calabi-Yau threefolds, birational geometry of symplectic resolutions of nilpotent orbits, moduli stacks of second-rank Giesker bundles with a fixed determinate on a nodal curve, vector bundles on curves and theta functions, Abelian varieties with bounded modular height, the moduli of regular holonomic Dx-modules with natural parabolic stability, cohomology groups of stable quasi-Abelian degenerations, semi-stable extensions on arithmetic surfaces, cusp form motives, polarized K3 surfaces, rigid geometry and applications, and moduli of stable parabolic conventions with Riemann-Hilbert correspondence and other features.
Peterson varieties are a type of regular nilpotent Hessenberg variety.
Among the topics are toward a Mackay formula for the compact restriction of character sheaves, constructing Hecke algebras associated to a Coxeter group, regularity and distinction of supercuspidal representations, and parametrizing nilpotent orbits in p-adic symmetric spaces.