Characterization of Normalizer of Lie Superalgebra and its Application to Control Theory
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911705035964416 |
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| author | Sahoo, Aroonima Pati, Kishor Chandra Khuntia, Tofan Kumar |
| author_facet | Sahoo, Aroonima Pati, Kishor Chandra Khuntia, Tofan Kumar |
| contents | The dynamical systems having both bosonic and fermionic variables play an important role in the theory of supersymmetry. This article addresses the control problems including both bosonic and fermionic variables on Lie supergroup as the configuration space. Here, the control systems are characterized using the normalizer of Lie subsuperalgebra of left-invariant vector fields in the Lie superalgebra of all smooth vector fields of Lie supergroup. Then, the linear control system is studied in detail and its controllability criterion is proposed along with suitable examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_22694 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterization of Normalizer of Lie Superalgebra and its Application to Control Theory Sahoo, Aroonima Pati, Kishor Chandra Khuntia, Tofan Kumar Optimization and Control Mathematical Physics 37N35, 58A50, 58C50, 93B05, 93C05 The dynamical systems having both bosonic and fermionic variables play an important role in the theory of supersymmetry. This article addresses the control problems including both bosonic and fermionic variables on Lie supergroup as the configuration space. Here, the control systems are characterized using the normalizer of Lie subsuperalgebra of left-invariant vector fields in the Lie superalgebra of all smooth vector fields of Lie supergroup. Then, the linear control system is studied in detail and its controllability criterion is proposed along with suitable examples. |
| title | Characterization of Normalizer of Lie Superalgebra and its Application to Control Theory |
| topic | Optimization and Control Mathematical Physics 37N35, 58A50, 58C50, 93B05, 93C05 |
| url | https://arxiv.org/abs/2605.22694 |