颂扬国家
发表于 2025-3-25 05:11:34
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ear-canal
发表于 2025-3-25 07:53:20
The Universal Enveloping AlgebraWe have seen that elements of the Lie algebra of a Lie group . are derivations of .. (.); that is, differential operators that are left-invariant. The universal enveloping algebra is the ring of all left-invariant differential operators, including higher-order ones. There is a purely algebraic construction of this ring.
DEI
发表于 2025-3-25 14:43:26
Representations of ,(2, ℂ)Unless otherwise indicated, in this chapter a . of a Lie group or Lie algebra is a complex representation.
连锁,连串
发表于 2025-3-25 17:40:52
The Universal CoverIf . is a Hausdorff topological space, a . is a continuous map . → . The path is . if the endpoints coincide: .(0) = .(1). A closed path is also called a .
美食家
发表于 2025-3-25 21:22:32
The Local Frobenius TheoremLet . be an .-dimensional smooth manifold. The . of . is the disjoint union of all tangent spaces of points of ..
PAEAN
发表于 2025-3-26 01:15:11
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不朽中国
发表于 2025-3-26 06:04:10
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llibretto
发表于 2025-3-26 12:01:53
Graduate Texts in Mathematicshttp://image.papertrans.cn/l/image/585692.jpg
上流社会
发表于 2025-3-26 16:29:54
Vector Fieldsen cover of . and such that, for each (.,ø) ∈ ., the image ø(.) of ø is an open subset of ℝ. and ø is a homeomorphism of . onto ø(.). We assume that if .,. ∈ ., then .. o ø..is a diffeomorphism from (. ∩ .) onto .. (. ∩ .). The set . is called a ..
单色
发表于 2025-3-26 18:40:54
Geodesics and Maximal Tori properties of geodesics in a Riemannian manifold and one using some algebraic topology. The reader will experience no loss of continuity if he reads one of these proofs and skips the other. The proof in this chapter is simpler and more self-contained.