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In mathematics, the nilpotent cone N {\displaystyle {\mathcal {N}}} of a finite-dimensional semisimple Lie algebra g {\displaystyle {\mathfrak {g}}} is...

In mathematics, nilpotent orbits are generalizations of nilpotent matrices that play an important role in representation theory of real and complex semisimple...

endomorphism a d x {\displaystyle ad_{x}} is a nilpotent endomorphism. 4.  A nilpotent cone normalizer The normalizer of a subspace K {\displaystyle K} of a Lie...

zero divisors, nilpotent elements, and idempotents. (For example, ⁠1/2⁠(1 + j) is an idempotent zero-divisor, and i − j is nilpotent.) As an algebra...

Gromov's theorem, a group of polynomial growth is virtually nilpotent, i.e. it has a nilpotent subgroup of finite index. In particular, the order of polynomial...

they are asymptotic cones (see Ultralimit) of finitely-generated nilpotent groups, and of nilpotent Lie groups, as well as tangent cones of sub-Riemannian...

\partial } of a commutative ring A {\displaystyle A} is called a locally nilpotent derivation (LND) if every element of A {\displaystyle A} is annihilated...

any discrete group with polynomial growth is virtually nilpotent (i.e. it contains a nilpotent subgroup of finite index). See Gromov's theorem on groups...

S-scheme T and a subscheme T 0 {\displaystyle T_{0}} of T given by a nilpotent ideal, X ( T ) → X ( T 0 ) {\displaystyle X(T)\to X(T_{0})} is surjective...

a torsion-free abelian group is bi-orderable; this is still true for nilpotent groups but there exist torsion-free, finitely presented groups which are...

Poisson and Martin boundaries are trivial for symmetric random walks in nilpotent groups. On the other hand, when the random walk is non-centered, the study...

said to be semisimple (resp. nilpotent) if ad ⁡ ( x ) {\displaystyle \operatorname {ad} (x)} is a semisimple (resp. nilpotent) operator. If x ∈ g {\displaystyle...

form a ring that is not a field. Another ring structure on P uses a nilpotent e to write x + y e for (x,y). The action of e on P reduces the plane to...

groups satisfy quadratic isoperimetric inequalities. A finitely generated nilpotent group has a Dehn function equivalent to nd where d ≥ 1 and all positive...

group on k18 whose ring of invariants is not finitely generated. Locally nilpotent derivation Bibliography Nagata, Masayoshi (1960) [1958], "On the fourteenth...

upper branch of the light cone, the future light cone. Q(x) = 0, x0 < 0 is the lower branch of the light cone, the past light cone. Q(x) < 0 is a hyperboloid...

Press. ISBN 978-0-521-62401-5. Uses synthetic differential geometry and nilpotent infinitesimals. Boelkins, M. (2012). Active Calculus: a free, open text...

{\displaystyle {\begin{pmatrix}p&q\\r&s\end{pmatrix}}} (but notice that any non-nilpotent scalar multiple of this matrix represents the same Laguerre transformation)...

{\displaystyle a^{n}=0} for some positive integer n {\displaystyle n} is called nilpotent. The localization of a ring is a process in which some elements are rendered...

composition of representing maps, and any element of non-zero degree is nilpotent (Nishida 1973). If f and g and h are elements of π ∗ S {\displaystyle...