Invariants of Lie color algebras acting on graded algebras

Jeffrey Bergen; Piotr Grzeszczuk

Colloquium Mathematicae (2000)

  • Volume: 83, Issue: 1, page 107-124
  • ISSN: 0010-1354

Abstract

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We prove a series of "going-up" theorems contrasting the structure of semiprime algebras and their subalgebras of invariants under the actions of Lie color algebras.

How to cite

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Bergen, Jeffrey, and Grzeszczuk, Piotr. "Invariants of Lie color algebras acting on graded algebras." Colloquium Mathematicae 83.1 (2000): 107-124. <http://eudml.org/doc/210766>.

@article{Bergen2000,
abstract = {We prove a series of "going-up" theorems contrasting the structure of semiprime algebras and their subalgebras of invariants under the actions of Lie color algebras.},
author = {Bergen, Jeffrey, Grzeszczuk, Piotr},
journal = {Colloquium Mathematicae},
keywords = {Lie color algebra; subalgebra of invariants; graded algebra; semiprime algebra; Artinian algebra; Goldie dimension; Krull dimension; Noetherian algebra},
language = {eng},
number = {1},
pages = {107-124},
title = {Invariants of Lie color algebras acting on graded algebras},
url = {http://eudml.org/doc/210766},
volume = {83},
year = {2000},
}

TY - JOUR
AU - Bergen, Jeffrey
AU - Grzeszczuk, Piotr
TI - Invariants of Lie color algebras acting on graded algebras
JO - Colloquium Mathematicae
PY - 2000
VL - 83
IS - 1
SP - 107
EP - 124
AB - We prove a series of "going-up" theorems contrasting the structure of semiprime algebras and their subalgebras of invariants under the actions of Lie color algebras.
LA - eng
KW - Lie color algebra; subalgebra of invariants; graded algebra; semiprime algebra; Artinian algebra; Goldie dimension; Krull dimension; Noetherian algebra
UR - http://eudml.org/doc/210766
ER -

References

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  1. [BG1] J. Bergen and P. Grzeszczuk, Invariants of Lie superalgebras acting on associative algebras, Israel J. Math. 94 (1996), 403-428. Zbl0863.16028
  2. [BG2] J. Bergen and P. Grzeszczuk, Gradings, derivations, and automorphisms of some algebras which are nearly associative, J. Algebra 179 (1996), 732-750. Zbl0859.17002
  3. [CR] M. Cohen and L. Rowen, Group graded rings, Comm. Algebra 11 (1983), 1253-1270. Zbl0522.16001
  4. [J] N. Jacobson, A note on automorphisms and derivations of Lie algebras, Proc. Amer. Math. Soc. 6 (1955), 281-283. Zbl0064.27002
  5. [M] S. Montgomery, Hopf Algebras and Their Actions on Rings, CBMS Regional Conf. Ser. in Math. 82, Amer. Math. Soc., Providence, RI, 1993. 
  6. [Sc] M. Scheunert, Generalized Lie algebras, J. Math. Phys. 20 (1979), 712-720. Zbl0423.17003

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