Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics. Verma modules can be used in the classification of irreducible representations of a complex semisimple Lie algebra. Specifically, although Verma modules themselves are infinite dimensional, quotients of them can be used to construct finite-dimensional representations with highest weight , where is dominant and integral. Their homomorphisms correspond to invariant differential operators over flag manifolds.
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| - Verma-Modul (de)
- 베르마 가군 (ko)
- Verma module (en)
- Verma模 (zh)
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| - In der Mathematik ist der Verma-Modul ein unendlich-dimensionaler Modul über der universellen einhüllenden Algebra einer Lie-Algebra, aus dem sich die endlich-dimensionalen Darstellungen eines gegebenen höchsten Gewichts gewinnen lassen. (de)
- Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics. Verma modules can be used in the classification of irreducible representations of a complex semisimple Lie algebra. Specifically, although Verma modules themselves are infinite dimensional, quotients of them can be used to construct finite-dimensional representations with highest weight , where is dominant and integral. Their homomorphisms correspond to invariant differential operators over flag manifolds. (en)
- 리 대수의 표현론에서 베르마 가군(वर्मा加群, 영어: Verma module)은 주어진 무게에 대한 가장 “일반적인” 최고 무게 가군이다. (ko)
- Verma模（Verma module）是李代數表示理論中的基本研究對象，其名取自。Verma模之間的態射相應於上的。 可用Verma模來證明以下命題：為的的維數有限，若且僅若是（dominant integral weight）。 (zh)
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| - BGG resolution (en)
- Verma module (en)
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| - In der Mathematik ist der Verma-Modul ein unendlich-dimensionaler Modul über der universellen einhüllenden Algebra einer Lie-Algebra, aus dem sich die endlich-dimensionalen Darstellungen eines gegebenen höchsten Gewichts gewinnen lassen. (de)
- Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics. Verma modules can be used in the classification of irreducible representations of a complex semisimple Lie algebra. Specifically, although Verma modules themselves are infinite dimensional, quotients of them can be used to construct finite-dimensional representations with highest weight , where is dominant and integral. Their homomorphisms correspond to invariant differential operators over flag manifolds. (en)
- 리 대수의 표현론에서 베르마 가군(वर्मा加群, 영어: Verma module)은 주어진 무게에 대한 가장 “일반적인” 최고 무게 가군이다. (ko)
- Verma模（Verma module）是李代數表示理論中的基本研究對象，其名取自。Verma模之間的態射相應於上的。 可用Verma模來證明以下命題：為的的維數有限，若且僅若是（dominant integral weight）。 (zh)
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