Restricted and quasi-toral restricted Lie-Rinehart algebras

Bing Sun; Liangyun Chen

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page 400-413
  • ISSN: 2391-5455

Abstract

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In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension should be.

How to cite

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Bing Sun, and Liangyun Chen. "Restricted and quasi-toral restricted Lie-Rinehart algebras." Open Mathematics 13.1 (2015): 400-413. <http://eudml.org/doc/275895>.

@article{BingSun2015,
abstract = {In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension should be.},
author = {Bing Sun, Liangyun Chen},
journal = {Open Mathematics},
keywords = {Restricted Lie-Rinehart algebras; Restrictable Lie-Rinehart algebras; Quasi-toral restricted Lie-Rinehart algebras; multiplicative 3-ary Hom-Nambu-Lie algebras; Rota-Baxter algebras; Hom-preLie algebras},
language = {eng},
number = {1},
pages = {400-413},
title = {Restricted and quasi-toral restricted Lie-Rinehart algebras},
url = {http://eudml.org/doc/275895},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Bing Sun
AU - Liangyun Chen
TI - Restricted and quasi-toral restricted Lie-Rinehart algebras
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 400
EP - 413
AB - In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension should be.
LA - eng
KW - Restricted Lie-Rinehart algebras; Restrictable Lie-Rinehart algebras; Quasi-toral restricted Lie-Rinehart algebras; multiplicative 3-ary Hom-Nambu-Lie algebras; Rota-Baxter algebras; Hom-preLie algebras
UR - http://eudml.org/doc/275895
ER -

References

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  13. [13] J. Huebschmann, Poisson cohomology and quantization. J. Reine Angew. Math. 408 (1990), 57-113. Zbl0699.53037
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  15. [15] R. Palais, The cohomology of Lie rings. Amer. Math. Soc., Providence, R. I., Proc. Symp. Pure Math. (1961), 130-137. [Crossref] 
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