Orbits of Free Cyclic Submodules Over Rings of Lower Triangular Matrices
| Autor: | Edyta Bartnicka |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Ring (mathematics)
Mathematics::Commutative Algebra Applied Mathematics 010102 general mathematics Triangular matrix Field (mathematics) General linear group Mathematics - Rings and Algebras 01 natural sciences 010101 applied mathematics Combinatorics Mathematics (miscellaneous) Rings and Algebras (math.RA) FOS: Mathematics Orbit (dynamics) 0101 mathematics Mathematics::Representation Theory Bell number Mathematics |
| Zdroj: | Results in Mathematics. 76 |
| ISSN: | 1420-9012 1422-6383 |
| DOI: | 10.1007/s00025-021-01420-7 |
| Popis: | Given a ring $$T_n\ (n\geqslant 2)$$ T n ( n ⩾ 2 ) of lower triangular $$n\times n$$ n × n matrices with entries from an arbitrary field F, we completely classify the orbits of free cyclic submodules of $$^2T_n$$ 2 T n under the action of the general linear group $$GL_2(T_n)$$ G L 2 ( T n ) . Interestingly, the total number of such orbits is found to be equal to the Bell number $$B_n$$ B n . A representative of each orbit is also given. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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