noncommutative invariant theory
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2019 ◽  
Vol 62 (3) ◽  
pp. 518-530 ◽  
Author(s):  
LIYU LIU ◽  
WEN MA

AbstractNakayama automorphisms play an important role in the fields of noncommutative algebraic geometry and noncommutative invariant theory. However, their computations are not easy in general. We compute the Nakayama automorphism ν of an Ore extension R[x; σ, δ] over a polynomial algebra R in n variables for an arbitrary n. The formula of ν is obtained explicitly. When σ is not the identity map, the invariant EG is also investigated in terms of Zhang’s twist, where G is a cyclic group sharing the same order with σ.


2017 ◽  
Vol 27 (07) ◽  
pp. 831-848 ◽  
Author(s):  
Mátyás Domokos ◽  
Vesselin Drensky

It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has a rational Hilbert series, and consequently the Hilbert series of the algebra of polynomial invariants of a group of linear transformations is rational, whenever this algebra is finitely generated. This basic principle is applied here to prove rationality of Hilbert series of algebras of invariants that are neither commutative nor finitely generated. Our main focus is on linear groups acting on certain factor algebras of the tensor algebra that arise naturally in the theory of polynomial identities.


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