Graded Lie
차등 거짓말

Graded Lie(차등 거짓말)란 무엇입니까?

Graded Lie 차등 거짓말 - In recent years, the representations of types B(m,n), C(n), D(m,n), P(n) and Q(n)-graded Lie superalgebras coordinatized by quantum tori have been studied. ^[1] In a previous paper by the authors, we obtain the first example of a finitely freely generated simple Z-graded Lie conformal algebra of linear growth that cannot be embedded into any general Lie conformal algebra. ^[2] The successive quotients correspond to homogenous elements of graded Lie algebras introduced by the author in an earlier work. ^[3] We extend some well known results in group theory to N -graded Lie algebras: for example, we show that one relator N -graded Lie algebras are iterated HNN extensions with free bases which can be used for cohomology computations and apply the Mayer-Vietoris sequence to give some results about coherence of Lie algebras. ^[4] As a by-product we determine a basis for the identities of certain graded Lie algebras with a grading in which every homogeneous subspace has dimension ≤ 1. ^[5] Let W(Γ) be a class of not-finitely graded Lie algebras related to generalized Virasoro algebras with basis {Lα,i,C | α∈Γ, i∈Z+}, which satisfies relations [Lα,i,L β,j]=(β-α)Lα+β,i+j+(j-i)L α+β,i+j. ^[6] It was subsequently shown that, upon appending additional vector spaces, this structure can be reinterpreted as a differential graded Lie algebra. ^[7] We prove that the string topology bracket on the $S^1$-equivariant homology $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ of the free loop space of X preserves the Hodge decomposition of $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $, making it a bigraded Lie algebra. ^[8] We generalize the P(N)-graded Lie superalgebras of Martinez-Zelmanov. ^[9] Working over various graded Lie algebras and in arbitrary dimension, we express scattering diagrams and theta functions in terms of counts of tropical curves/disks, weighted by multiplicities given in terms of iterated Lie brackets. ^[10] In this paper, we investigate critical Gagliardo–Nirenberg, Trudinger-type and Brezis–Gallouet–Wainger inequalities associated with the positive Rockland operators on graded Lie groups, which include the cases of [Formula: see text], Heisenberg, and general stratified Lie groups. ^[11] Like the lower central series of a nilpotent group, filters generalize the connection between nilpotent groups and graded Lie rings. ^[12] This is done by finding a realization of a Z2-graded Lie superalgebra in terms of a standard Lie superalgebra and the Clifford algebra. ^[13] Such analysis can be conveniently realised in the setting of graded Lie groups. ^[14] We describe the multiplicative structures and the coordinate algebras of ( Θ n , sl n ) -graded Lie algebras for n ≥ 5 , classify these Lie algebras and determine their central extensions. ^[15] In this paper, dedicated to the memory of Kirill Mackenzie, I relate the origins and early development of the theory of graded Lie brackets, first in the publications on differential geometry of Schouten, Nijenhuis, and Frolicher–Nijenhuis, then in the work of Gerstenhaber and Nijenhuis–Richardson in cohomology theory. ^[16] This paper presents the classification, over the fields of real and complex numbers, of the minimal Z2 × Z2-graded Lie algebras and Lie superalgebras spanned by 4 generators and with no empty graded sector. ^[17] In particular, we show Fujita exponent for the Rockland heat equation on graded Lie group, which depends on the homogeneous dimension of group and the order of the Rockland operator. ^[18] Kostant, Graded manifolds, graded Lie theory and prequantization, Springer, Berlin, 1977, [18], Leites, Usp Math Nauk 35:3–57, 1980, [19]). ^[19] Using the Gerstenhaber bracket and alternating Schouten product, differential graded Lie algebra are constructed on the space of multilinear mappings of Hom-associative H-pseudoalgebra and Hom-Lie H-pseudoalgebras. ^[20] The graded Lie brackets are constructed by means of a derivation and involution of commutative superalgebra, and we use them to construct 3-Lie superalgebras. ^[21] We study the lower central series of a right-angled Coxeter group \({\rm{R}}{{\rm{C}}_{\cal K}}\) and the associated graded Lie algebra \(L\left( {{\rm{R}}{{\rm{C}}_{\cal K}}} \right)\). ^[22] We give an explicit proof of the theorems which state that the space Gra is a well\/-\/defined differential graded Lie algebra: both the Lie bracket $[{\cdot},{\cdot}]$ and the vertex\/-\/expanding differential ${\mathrm d}=[{\bullet}\!{-}\!{\bullet},{\cdot}]$ respect the calculus modulo zero graphs. ^[23] We prove that a differential graded Lie algebra is homotopy abelian if its adjoint map into its cochain complex of derivations is trivial in cohomology. ^[24] We provide two criteria for discarding the formality of a differential graded Lie algebra in terms of higher Whitehead brackets, which are the Lie analogue of the Massey products of a differential graded associative algebra. ^[25] In this paper we show blow-up of solutions of the nonlinear heat equation with the Rockland operators on the graded Lie groups. ^[26] Using a method of Uchino, we construct an explicit graded Lie algebra whose Maurer-Cartan elements are given by $\mathcal{O}$-operators. ^[27] Inverse problems of identifying the coefficients of right hand side of the pseudo-parabolic equation from the local overdetermination condition have important applications in various areas of applied science and engineering, also such problems can be modeled using common homogeneous left-invariant hypoelliptic operators on common graded Lie groups. ^[28] We present a novel realization of the Z2×Z2-graded Lie superalgebra gl(m1,m2|n1,n2) inside an algebraic extension of the enveloping algebra of the Z2-graded Lie superalgebra gl(m|n), with m = m1 + m2 and n = n1 + n2. ^[29] In this note, we interpret Leibniz algebras as differential graded Lie algebras. ^[30] On the one hand, $${\mathcal{O}}$$O-operators are shown to be characterized as the Maurer–Cartan elements in a suitable graded Lie algebra. ^[31] We provide the symmetries explicitly and compute, via the first Spencer cohomology groups, the Tanaka-Weisfeiler prolongation of the negatively graded Lie superalgebras associated with two particular choices of parabolics. ^[32] We consider finite-dimensional irreducible transitive graded Lie algebras L = ∑ i = − q r L i over algebraically closed fields of characteristic three. ^[33] Fof a nilpotent differential graded Lie algebra whose components vanish in degrees below -1 we construct an explicit equivalence between the nerve of the Deligne 2-groupoid and the simplicial set of differential forms with values in the Lie algebra introduced by V. ^[34] We do so by analyzing the asymptotic behavior of Maurer-Cartan elements of a differential graded Lie algebra constructed from a (not-necessarily tropical) monoid-graded Lie algebra. ^[35] In this paper, we show that there are only seven graded Lie algebras of dimension 5 generated in degree 1 up to isomorphism. ^[36] Such a geometric method allows us to classify nilpotent Lie algebras of small dimensions, as well as to classify narrow naturally graded Lie algebras. ^[37] The other one is no longer a Z2-graded Lie superalgebra but a Z2 × Z2-graded Lie superalgebra, a rather different algebraic structure, denoted here by pso(2m + 1|2n). ^[38] We establish a correspondence between infinity-enhanced Leibniz algebras, recently introduced in order to encode tensor hierarchies, and differential graded Lie algebras, which have been already used in this context. ^[39] In this paper, we prove that a natural candidate for a homogeneous norm on a graded Lie algebra of length 5 satisfies the triangle inequality which answers Moskowitz's question. ^[40] An early mathematically rigorous treatment of super Lie groups is presented in Kostant (Graded manifolds, graded Lie theory, and prequantization. ^[41] We show that this tensor hierarchy can be canonically equipped with a differential graded Lie algebra structure that coincides with the one that is found in supergravity theories. ^[42] As an application, we prove that the infinitesimal deformation theory of a derived complex analytic moduli problem is governed by a differential graded Lie algebra. ^[43] This paper considers the analogues of Green-type formulae for Rockland operators on graded Lie groups. ^[44] Quillen showed how to describe the homotopy theory of simply-connected rational spaces in terms of differential graded Lie algebras. ^[45] The group G is said to be filtered-formal if its Malcev Lie algebra is isomorphic to the degree completion of its associated graded Lie algebra. ^[46]
최근에는 양자 토리에 의해 조정된 유형 B(m,n), C(n), D(m,n), P(n) 및 Q(n) 등급 거짓말 초대수학의 표현이 연구되었습니다. ^[1] 저자의 이전 논문에서 우리는 어떤 일반적인 Lie 등각 대수에 포함될 수 없는 선형 성장의 유한하게 자유롭게 생성된 간단한 Z-등급 Lie 등각 대수의 첫 번째 예를 얻습니다. ^[2] 연속적인 몫은 저자가 이전 작업에서 소개한 단계별 거짓말 대수학의 동질 요소에 해당합니다. ^[3] 우리는 그룹 이론의 일부 잘 알려진 결과를 N 등급 거짓말 대수로 확장합니다. 예를 들어, 하나의 관계자 N 등급 거짓말 대수는 코호몰로지 계산에 사용될 수 있고 Mayer-Vietoris 시퀀스를 적용할 수 있는 자유 염기가 있는 반복 HNN 확장임을 보여줍니다. 거짓말 대수의 일관성에 대한 몇 가지 결과를 제공합니다. ^[4] 부산물로 우리는 모든 동질 부분 공간이 차원 ≤ 1을 갖는 등급을 사용하여 등급이 매겨진 거짓말 대수학의 ID에 대한 기초를 결정합니다. ^[5] W(Γ)를 기본 {Lα,i,C | α∈Γ, i∈Z+}, 관계식 [Lα,i,Lβ,j]=(β-α)Lα+β,i+j+(j-i)Lα+β,i+j를 만족합니다. ^[6] 추가 벡터 공간을 추가하면 이 구조가 차등 등급 거짓말 대수로 재해석될 수 있다는 것이 이후에 나타났습니다. ^[7] 우리는 $S^1$-등가 상동성 $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\ mathbb {Q}}) X의 자유 루프 공간의 $는 $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X, {\mathbb {Q}}) $, 큰 거짓말 대수를 만듭니다. ^[8] 우리는 Martinez-Zelmanov의 P(N) 등급 거짓말 대수학을 일반화합니다. ^[9] 다양한 등급의 거짓말 대수학 및 임의 차원에서 작업하면서, 우리는 반복된 거짓말 괄호로 주어진 다중도에 의해 가중치가 부여된 열대 곡선/원반의 수로 산란 다이어그램과 세타 함수를 표현합니다. ^[10] 이 논문에서 우리는 [공식: 텍스트 참조], Heisenberg 및 일반 계층화된 거짓말의 경우를 포함하는 등급화된 거짓말 그룹에 대한 양의 Rockland 연산자와 관련된 중요한 Gagliardo-Nirenberg, Trudinger-type 및 Brezis-Gallouet-Wainger 부등식을 조사합니다. 여러 떼. ^[11] nilpotent 그룹의 아래쪽 중앙 계열과 마찬가지로 필터는 nilpotent 그룹과 등급이 지정된 Lie ring 간의 연결을 일반화합니다. ^[12] 이것은 표준 Lie superalgebra 및 Clifford algebra의 관점에서 Z2 등급 Lie superalgebra의 실현을 찾는 것으로 수행됩니다. ^[13] 이러한 분석은 차등화된 Lie 그룹 설정에서 편리하게 실현할 수 있습니다. ^[14] 우리는 n ≥ 5에 대한 ( Θ n , sl n ) 등급 거짓말 대수의 승법 구조와 좌표 대수를 설명하고 이러한 거짓말 대수를 분류하고 중심 확장을 결정합니다. ^[15] Kirill Mackenzie를 기리는 이 논문에서 나는 먼저 Schouten, Nijenhuis 및 Frolicher-Nijenhuis의 미분 기하학에 관한 출판물에서, 그 다음에는 Gerstenhaber의 작업에서 차등 거짓말 괄호 이론의 기원과 초기 발전에 대해 설명합니다. 그리고 코호몰로지 이론의 Nijenhuis-Richardson. ^[16] 이 논문은 4개의 생성기에 걸쳐 있고 빈 등급 섹터가 없는 최소 Z2 × Z2 등급 거짓말 대수 및 거짓말 초대수학의 실수 및 복소수 필드에 대한 분류를 제시합니다. ^[17] 특히, 우리는 그룹의 균질 차원과 Rockland 연산자의 차수에 의존하는 등급화된 Lie 그룹에 대한 Rockland 열 방정식에 대한 Fujita 지수를 보여줍니다. ^[18] Kostant, 등급화된 다양체, 등급화된 거짓말 이론 및 사전 양자화, Springer, Berlin, 1977, [18], Leites, Usp Math Nauk 35:3–57, 1980, [19]). ^[19] Gerstenhaber 브래킷과 교대 Schouten 곱을 사용하여 Hom-associative H-pseudoalgebra 및 Hom-Lie H-pseudoalgebras의 다중 선형 매핑 공간에 차등 등급 거짓말 대수를 구성합니다. ^[20] 등급이 있는 거짓말 괄호는 가환성 대수학의 파생 및 내포를 통해 구성되며 이를 사용하여 3-거짓 대수학을 구성합니다. ^[21] 우리는 직각 Coxeter 그룹 \({\rm{R}}{{\rm{C}}_{\cal K}}\) 및 관련 등급 거짓말 대수 \(L\left ( {{\rm{R}}{{\rm{C}}_{\cal K}}} \right)\). ^[22] 우리는 공간 Gra이 잘 정의된 미분 등급 거짓말 대수임을 명시하는 정리의 명시적 증거를 제공합니다. 거짓말 괄호 $[{\cdot},{\cdot}]$ 및 정점 -\/확장 미분 ${\mathrm d}=[{\bullet}\!{-}\!{\bullet},{\cdot}]$ 미적분 모듈로 0 그래프를 따릅니다. ^[23] 우리는 미분 등급의 거짓말 대수가 동형 사슬형 파생물에 대한 인접 맵이 ​​코호몰로지에서 사소한 경우 동형 아벨임을 증명합니다. ^[24] 우리는 차등 등급 결합 대수학의 Massey 제품의 거짓말 유사체인 더 높은 Whitehead 브래킷 측면에서 차등 등급 거짓말 대수의 형식을 폐기하기 위한 두 가지 기준을 제공합니다.