Locally finite and locally nilpotent derivations with applications to polynomial flows, morphisms and 𝒢ₐ-actions. II

Essen, Arno van den

doi:10.1090/s0002-9939-1994-1185282-0

Cited by 12 publications

(1 citation statement)

References 21 publications

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“…t z , which has been studied in [8][9][10]31,30] for the commutative case. The last two components of Ω F t are given directly as…”

Section: Ncs Systems Over Differential Operator Algebrasmentioning

confidence: 99%

Noncommutative symmetric systems over associative algebras

Zhao

2007

Journal of Pure and Applied Algebra

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This paper is the first of a sequence of papers [W. Zhao, Differential operator specializations of noncommutative symmetric functions (submitted for publication). math.CO/0509134; W. Zhao, Noncommutative symmetric functions and the inversion problem (submitted for publication). math.CV/0509135; W. Zhao, A NCS system over the Grossman-Larson Hopf algebra of labeled rooted trees (submitted for publication). math.CO/0509136; W. Zhao, NCS systems over differential operator algebras and the Grossman-Larson Hopf algebra of labeled rooted trees (submitted for publication). math.CO/0509138. preprint] on the NCS (noncommutative symmetric) systems over differential operator algebras in commutative or noncommutative variables [W. Zhao, Differential operator specializations of noncommutative symmetric functions (submitted for publication). math.CO/0509134]; the NCS systems over the Grossman-Larson

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“…t z , which has been studied in [8][9][10]31,30] for the commutative case. The last two components of Ω F t are given directly as…”

Section: Ncs Systems Over Differential Operator Algebrasmentioning

confidence: 99%

Noncommutative symmetric systems over associative algebras

Zhao

2007

Journal of Pure and Applied Algebra

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Locally Nilpotent Derivations over a UFD and an Application to Rank Two Locally Nilpotent Derivations ofk[X1,…,X]

Daigle

Freudenburg

1998

Journal of Algebra

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Differential operator specializations of noncommutative symmetric functions

Zhao

2007

Advances in Mathematics

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Let K be any unital commutative Q-algebra and z = (z 1 , ..., z n ) commutative or noncommutative free variables. Let t be a formal parameter which commutes with z and elements of K. We denote uniformly by K z and K[[t]] z the formal power series algebras of z over K and K[[t]], respectively. For any α ≥ 1, let D [α] z be the unital algebra generated by the differential operators of K z which increase the degree in z by at least α − 1 and Az , we introduce five sequences of differential operators of K z and show that their generating functions form a NCS (noncommutative symmetric) system ([Z4]) over the differential algebra D [α] z . Consequently, by the universal property of the NCS system formed by the generating functions of certain NCSFs (noncommutative symmetric functions) first introduced in [GKLLRT], we obtain a family of Hopf algebra homomorphisms S Ft :, which are also grading-preserving when F t satisfies certain conditions. Note that, the homomorphisms S Ft above can also be viewed as specializations of NCSFs by the differential operators of K z . Secondly, we show that, in both commutative and noncommutative cases, this family S Ft (with all n ≥ 1 and F t ∈ A[α] t z ) of differential operator specializations can distinguish any two different NCSFs. Some connections of the results above with the quasi-symmetric functions ([Ge], [MR], [S]) are also discussed.

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Locally finite and locally nilpotent derivations with applications to polynomial flows, morphisms and 𝒢ₐ-actions. II

Cited by 12 publications

References 21 publications

Noncommutative symmetric systems over associative algebras

Noncommutative symmetric systems over associative algebras

Locally Nilpotent Derivations over a UFD and an Application to Rank Two Locally Nilpotent Derivations ofk[X1,…,X]

Differential operator specializations of noncommutative symmetric functions

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