Small modules with interesting rank varieties
This paper focuses on the rank varieties for modules over a group algebra FE where E is an elementary abelian p-group and p is the characteristic of an algebraically closed field F. In the first part, we give a sufficient condition for a Green vertex of an indecomposable module to contain an element...
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| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/170882 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | This paper focuses on the rank varieties for modules over a group algebra FE where E is an elementary abelian p-group and p is the characteristic of an algebraically closed field F. In the first part, we give a sufficient condition for a Green vertex of an indecomposable module to contain an elementary abelian p-group E in terms of the rank variety of the module restricted to E. In the second part, given a homogeneous algebraic variety V, we explore the problem on finding a small module with rank variety V. In particular, we examine the simple module D(kp−p+1,1p−1) for the symmetric group Skp. |
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