Invariant Hermitian lattices in the steinberg module and their isometry groups

K. S. Abdukhalikov

doi:10.1080/00927879708826010

Invariant Hermitian lattices in the steinberg module and their isometry groups

K. S. Abdukhalikov

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

The invariant Hermitian lattices in the Steinberg module of SL₂(q) are described. These lattices are connected with generalized quadratic residue codes over a field of four elements. The isometry groups of invariant lattices are calculated. In particular, 13-dimensional unimodular lattices over Eisenstein numbers with minimum norm 3 and automorphism group Z₆ × PS_P6(3) are obtained.

Original language	English
Pages (from-to)	2607-2626
Number of pages	20
Journal	Communications in Algebra
Volume	25
Issue number	8
DOIs	https://doi.org/10.1080/00927879708826010
Publication status	Published - 1997
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927879708826010

Cite this

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title = "Invariant Hermitian lattices in the steinberg module and their isometry groups",

abstract = "The invariant Hermitian lattices in the Steinberg module of SL2(q) are described. These lattices are connected with generalized quadratic residue codes over a field of four elements. The isometry groups of invariant lattices are calculated. In particular, 13-dimensional unimodular lattices over Eisenstein numbers with minimum norm 3 and automorphism group Z6 × PSP6(3) are obtained.",

author = "Abdukhalikov, {K. S.}",

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year = "1997",

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AU - Abdukhalikov, K. S.

N1 - Funding Information: 'This research was partially supported by International Science Foundation grant MYJOOO

PY - 1997

Y1 - 1997

N2 - The invariant Hermitian lattices in the Steinberg module of SL2(q) are described. These lattices are connected with generalized quadratic residue codes over a field of four elements. The isometry groups of invariant lattices are calculated. In particular, 13-dimensional unimodular lattices over Eisenstein numbers with minimum norm 3 and automorphism group Z6 × PSP6(3) are obtained.

AB - The invariant Hermitian lattices in the Steinberg module of SL2(q) are described. These lattices are connected with generalized quadratic residue codes over a field of four elements. The isometry groups of invariant lattices are calculated. In particular, 13-dimensional unimodular lattices over Eisenstein numbers with minimum norm 3 and automorphism group Z6 × PSP6(3) are obtained.

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DO - 10.1080/00927879708826010

M3 - Article

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JO - Communications in Algebra

JF - Communications in Algebra

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Invariant Hermitian lattices in the steinberg module and their isometry groups

Abstract

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