IJPAM: Volume 49, No. 1 (2008)

FAMILIES OF ALGEBRAIC LATTICES IN
EVEN DIMENSIONS UP TO 8

Agnaldo José Ferrari$^1$, Antonio Aparecido de Andrade$^2$
$^{1,2}$Department of Mathematics
UNESP - State University of São Paulo at São José do Rio Preto
Rua Cristovão Colombo, 2265, Jardim Nazareth
São José do Rio Preto, SP, 15054-000, BRAZIL
$^1$e-mail: agnaldoferrari@ig.com.br
$^2$e-mail: andrade@ibilce.unesp.br


Abstract.In this paper, starting from suitable ideals in the ring of algebraic integers of cyclotomic fields $\matQ(\zeta_m)$, where $m=3,6,8,9,20$, we present new rotated versions of lattices in dimensions $2$, $4$, $6$ and $8$, by use of the canonical homomorphism. These rotated versions reproduce densest algebraic lattices in dimensions $2$, $4$, $6$ and $8$.

Received: August 2, 2008

AMS Subject Classification: 11T71, 94B05, 94B40

Key Words and Phrases: number fields, cyclotomic fields, quadratic forms, algebraic lattices, center density

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 1