The trace codimensions give a quantitative description of the identities satisfied by an algebra with trace. Here we study the asymptotic behaviour of the sequence of trace codimensions c tr n(A) and of pure trace codimensions c ptr n (A) of a finite-dimensional algebra A over a field of characteristic zero. We find an upper and lower bound of both codimensions and as a consequence we get that the limits limn→∞ctrn(A)√n and limn→∞cptrn(A) √n always exist and are integers. This result gives a positive answer to a conjecture of Amitsur in this setting. Finally we characterize the varieties of algebras whose exponential growth is bounded by 2

Giambruno A., Ioppolo A., La Mattina D. (2023). Trace Codimensions of Algebras and Their Exponential Growth. ISRAEL JOURNAL OF MATHEMATICS, 254(1), 431-459 [10.1007/s11856-022-2414-3].

Trace Codimensions of Algebras and Their Exponential Growth

La Mattina D.
2023-01-01

Abstract

The trace codimensions give a quantitative description of the identities satisfied by an algebra with trace. Here we study the asymptotic behaviour of the sequence of trace codimensions c tr n(A) and of pure trace codimensions c ptr n (A) of a finite-dimensional algebra A over a field of characteristic zero. We find an upper and lower bound of both codimensions and as a consequence we get that the limits limn→∞ctrn(A)√n and limn→∞cptrn(A) √n always exist and are integers. This result gives a positive answer to a conjecture of Amitsur in this setting. Finally we characterize the varieties of algebras whose exponential growth is bounded by 2
2023
Settore MAT/02 - Algebra
Giambruno A., Ioppolo A., La Mattina D. (2023). Trace Codimensions of Algebras and Their Exponential Growth. ISRAEL JOURNAL OF MATHEMATICS, 254(1), 431-459 [10.1007/s11856-022-2414-3].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/583670
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