A representation of range decreasing group homomorphisms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910920206188544 |
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| author | Zhang, Ning Liu, Lifan |
| author_facet | Zhang, Ning Liu, Lifan |
| contents | The method of range decreasing group homomorphisms can be applied to study various maps between mapping spaces, includin holomorphic maps, group homomorphisms, linear maps, semigroup homomorphisms, Lie algebra homomorphisms and algebra homomorphisms [Z1, Z2]. Previous studies on range decreasing group homomorphisms have primarily focused on specific subsets of mapping groups. In this paper, we provide a characterization of a general range decreasing group homomorphism applicable to the entire mapping group. As applications, we compute a particular class of homomorphisms between mapping groups and identify all range decreasing group homomorphisms defined on specific mapping groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17459 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A representation of range decreasing group homomorphisms Zhang, Ning Liu, Lifan Group Theory Differential Geometry 58D15, 22E65, 47B33, 58A05, 46T05 The method of range decreasing group homomorphisms can be applied to study various maps between mapping spaces, includin holomorphic maps, group homomorphisms, linear maps, semigroup homomorphisms, Lie algebra homomorphisms and algebra homomorphisms [Z1, Z2]. Previous studies on range decreasing group homomorphisms have primarily focused on specific subsets of mapping groups. In this paper, we provide a characterization of a general range decreasing group homomorphism applicable to the entire mapping group. As applications, we compute a particular class of homomorphisms between mapping groups and identify all range decreasing group homomorphisms defined on specific mapping groups. |
| title | A representation of range decreasing group homomorphisms |
| topic | Group Theory Differential Geometry 58D15, 22E65, 47B33, 58A05, 46T05 |
| url | https://arxiv.org/abs/2504.17459 |