笨拙的我
发表于 2025-3-23 13:27:30
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预知
发表于 2025-3-23 17:23:01
Lie Algebras,ce to the identity. The resulting object is called a Lie algebra. Simply by virtue of the fact that vector spaces are simpler than groups, the Lie algebra provides a powerful tool for studying Lie groups and their representations.
字的误用
发表于 2025-3-23 20:12:29
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不持续就爆
发表于 2025-3-23 22:19:02
Highest Weight Theory, Two important problems remain. The first is to parametrize Ĝ in a reasonable manner and the second is to individually construct each irreducible representation in a natural way. The solution to both of these problems is closely tied to the notion of . weights.
使更活跃
发表于 2025-3-24 05:32:35
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跳脱衣舞的人
发表于 2025-3-24 07:25:36
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cortisol
发表于 2025-3-24 12:50:49
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笨拙的你
发表于 2025-3-24 15:54:52
https://doi.org/10.1007/978-3-322-94211-1By examining the joint eigenvalues of a Cartan subalgebra under the ad-action, a great deal of information about a Lie group and its Lie algebra may be encoded. For instance, the fundamental group can be read off from this data (§ 6.3.3). Moreover, this encoding is a key step in the classification of irreducible representations (§7).
Encumber
发表于 2025-3-24 19:06:35
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CHAFE
发表于 2025-3-25 00:27:18
Representations,Lie groups are often the abstract embodiment of symmetry. However, most frequently they manifest themselves through an action on a vector space which will be called a representation. In this chapter we confine ourselves to the study of finite-dimensional representations.