Codimension growth of two-dimensional algebras

Antonino Giambruno; Mikhail Zaicev; null Giambruno; Sergey Mishchenko

Codimension growth of two-dimensional algebras

Antonino Giambruno, Mikhail Zaicev, Giambruno, Sergey Mishchenko

Matematica e Informatica

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Abstract

Let F be a field of characteristic zero and let A be a two-dimensional non-associative algebra over F. We prove that the sequence c_n(A), n=1, 2, . . . , of codimensions of A is either bounded by n + 1 or grows exponentially as 2^n. We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is n + 1, n ≥ 2.

Lingua originale	English
pagine (da-a)	3405-3415
Numero di pagine	11
Rivista	Proceedings of the American Mathematical Society
Volume	135
Stato di pubblicazione	Published - 2007

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All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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Giambruno, A., Zaicev, M., Giambruno, & Mishchenko, S. (2007). Codimension growth of two-dimensional algebras. Proceedings of the American Mathematical Society, 135, 3405-3415.

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abstract = "Let F be a field of characteristic zero and let A be a two-dimensional non-associative algebra over F. We prove that the sequence c_n(A), n=1, 2, . . . , of codimensions of A is either bounded by n + 1 or grows exponentially as 2^n. We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is n + 1, n ≥ 2.",

author = "Antonino Giambruno and Mikhail Zaicev and Giambruno and Sergey Mishchenko",

year = "2007",

language = "English",

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pages = "3405--3415",

journal = "Proceedings of the American Mathematical Society",

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T1 - Codimension growth of two-dimensional algebras

AU - Giambruno, Antonino

AU - Zaicev, Mikhail

AU - Giambruno, null

AU - Mishchenko, Sergey

PY - 2007

Y1 - 2007

N2 - Let F be a field of characteristic zero and let A be a two-dimensional non-associative algebra over F. We prove that the sequence c_n(A), n=1, 2, . . . , of codimensions of A is either bounded by n + 1 or grows exponentially as 2^n. We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is n + 1, n ≥ 2.

AB - Let F be a field of characteristic zero and let A be a two-dimensional non-associative algebra over F. We prove that the sequence c_n(A), n=1, 2, . . . , of codimensions of A is either bounded by n + 1 or grows exponentially as 2^n. We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is n + 1, n ≥ 2.

UR - http://hdl.handle.net/10447/13813

M3 - Article

VL - 135

SP - 3405

EP - 3415

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -

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