Trace forms of certain subfields of cyclotomic fields and applications
| Autor: | Agnaldo José Ferrari, Jos 'e Carmelo Interlando, Antonio Aparecido de Andrade, Robson Ricardo de Araujo |
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| Přispěvatelé: | Universidade Estadual Paulista (Unesp), São Paulo Federal Institute at Cubatão, San Diego University |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Trace (linear algebra) Euclidean space lcsh:Mathematics Cyclotomic fields High Energy Physics::Lattice Algebraic lattices Center (category theory) Signal design lcsh:QA1-939 Lambda Product (mathematics) Discrete Mathematics and Combinatorics Homomorphism Algebraic number Twisted homomorphism Gramian matrix Mathematics |
| Zdroj: | Scopus Repositório Institucional da UNESP Universidade Estadual Paulista (UNESP) instacron:UNESP Journal of Algebra Combinatorics Discrete Structures and Applications, Vol 7, Iss 2 (2020) |
| ISSN: | 2148-838X |
| DOI: | 10.13069/jacodesmath.729440 |
| Popis: | Made available in DSpace on 2020-12-12T02:12:06Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-05-07 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) In this work, we present a explicit trace forms for maximal real subfields of cyclotomic fields as tools for constructing algebraic lattices in Euclidean space with optimal center density. We also obtain a closed formula for the Gram matrix of algebraic lattices obtained from these subfields. The obtained lattices are rotated versions of the lattices Λ9, Λ10 and Λ11 and they are images of Z-submodules of rings of integers under the twisted homomorphism, and these constructions, as algebraic lattices, are new in the literature. We also obtain algebraic lattices in odd dimensions up to 7 over real subfields, calculate their minimum product distance and compare with those known in literatura, since lattices constructed over real subfields have full diversity. Department of Mathematics School of Sciences São Paulo State University (Unesp) Department of Mathematics Institute of Biosciences Humanities and Exact Sciences (Ibilce) São Paulo State University (Unesp) São Paulo Federal Institute at Cubatão Department of Mathematics & Statistics San Diego University Department of Mathematics School of Sciences São Paulo State University (Unesp) Department of Mathematics Institute of Biosciences Humanities and Exact Sciences (Ibilce) São Paulo State University (Unesp) CNPq: 429346/2018-2 |
| Databáze: | OpenAIRE |
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