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新疆大学数学与系统科学学院
Published:2024
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[1]张佳信,古丽沙旦木·玉奴斯.q-Heisenberg代数的Gr?bner-Shirshov基及结构性质[J].新疆大学学报(自然科学版中英文),2024,41(05):550-555+561.
[1]张佳信,古丽沙旦木·玉奴斯.q-Heisenberg代数的Gr?bner-Shirshov基及结构性质[J].新疆大学学报(自然科学版中英文),2024,41(05):550-555+561. DOI: 10.13568/j.cnki.651094.651316.2023.12.22.0002.
DOI:10.13568/j.cnki.651094.651316.2023.12.22.0002.
设n是正整数
q是非零的复数
hn(q)是q-Heisenberg代数.首先通过计算拟交换关系间的所有合成给出了hn(q)的极小Gr?bner-Shirshov基
并取关于此Gr?bner-Shirshov基的不可约元素构造了hn(q)的PBW基
然后证明了hn(q)的一些结构性质.
Let n be a positive integer
q a non-zero complex number
and hn(q) a q-Heisenberg algebra. In this paper
we first give the minimal Gr?bner-Shirshov basis of hn(q) by calculating all the compositions between the skew commutator relations
and construct the PBW basis of hn(q) by taking the irreducible elements about this Gr?bner-Shirshov basis. Then we prove some structural properties of hn(q).
BUCHBERGER B.An algorithm for finding a basis for the residue class ring of a zero-dimensional ideal[D].Austria:University of Innsbruck,1965.
BERGMAN G M.The diamond lemma for ring theory[J].Advances in Mathematics,1978,29(2):178-218.
SHIRSHOV A I.Some algorithmic problems for Lie algebras[M]//BOKUT L,SHESTAKOV I,LATYSHEV V,et al.Selected works of Shirshov AI,Basel:Birkha¨user Basel,2009:125-130.
BOKUT′L A.Embeddings into simple associative algebras[J].Algebra and Logic,1976,15(2):73-90.
KANG S J,LEE K H.Gr?bner-Shirshov bases for representation theory[J].Journal of the Korean Mathematical Society,2000,37:55-72.
CHIBRIKOV E S.On free Lie conformal algebras[J].Vestnik Novosibirsk State University,2004,4(1):65-83.
张海山.Heisenberg李代数的自同构群及典范Kac-Moody代数与可积模的完全可约性[D].北京:首都师范大学,2003.ZHANG H S.The automorphism groups of Heisenberg Lie algbras and the standard Kac-Moody algebras and the completely reducible of integrable modules[D].Beijing:Capital Normal University,2003.(in Chinese)
姬广智.Heisenberg李代数的Rota-Baxter算子[D].哈尔滨:哈尔滨理工大学,2019.JI G Z.Algebr Rota-Baxter operators of Heisenberg Lie algebra[D].Harbin:Harbin University of Science and Technology,2019.(in Chinese)
周春莹.Heisenberg李代数的自同构及拟自同构[D].苏州:苏州科技大学,2021.ZHOU C Y.The quasi-automorphism and automorphism of Heisenberg Lie algebras[D].Suzhou:Suzhou University of Science and Technology,2021.(in Chinese)
KANDRI-RODY A,WEISPFENNING V.Non-commutative Gr?bner bases in algebras of solvable type[J].Journal of Symbolic Computation,1990,9(1):1-26.
BOKUT L,CHEN Y Q,KALORKOTI K,et al.Gro¨bner-Shirshov bases:Normal forms,combinatorial,and decision problems in algebra[M].New Jersey:World Scientific,2018.
LI H S.Noncommutative Gr?bner bases and filtered-graded transfer[M].Berlin,Heidelberg:Springer Berlin Heidelberg,2002.
KRAUSE G R,LENAGAN T H.Growth of algebras and Gelfand-Kirillov dimension[M].Rhode Island:American Mathematical Society,2000.
LI H S.Gro¨bner bases in ring theory[M].Singapore:World Scientific,2011.
LI H S.An elimination lemma for algebras with PBW bases[J].Communications in Algebra,2018,46(8):3520-3532.
LEVANDOVSKYY V,SCHONEMANN H.Plural:A computer algebra system for noncommutative polynomial algebras[C]//Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation.New York:Association for Computing Machinery,2003:176-183.
LI H S.Noncommutative polynomial algebras of solvable type and their modules[M].Boca Raton:Chapmanand Hall/CRC,2021.
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