Report
Cohomologies and crossed modules for pre-Lie Rinehart algebras
| العنوان: | Cohomologies and crossed modules for pre-Lie Rinehart algebras |
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| المؤلفون: | Chen, Liangyun, Liu, Meijun, Liu, Jiefeng |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Rings and Algebras, Mathematics - Quantum Algebra, 17A30, 17A65, 17B63 |
| الوصف: | A pre-Lie-Rinehart algebra is an algebraic generalization of the notion of a left-symmetric algebroid. We construct pre-Lie-Rinehart algebras from r-matrices through Lie algebra actions. We study cohomologies of pre-Lie-Rinehart algebras and show that abelian extensions of pre-Lie-Rinehart algebras are classified by the second cohomology groups. We introduce the notion of crossed modules for pre-Lie-Rinehart algebras and show that they are classified by the third cohomology groups of pre-Lie-Rinehart algebras. At last, we use (pre-)Lie-Rinehart 2-algebras to characterize the crossed modules for (pre-)Lie Rinehart algebras. Comment: 23 pages, we add a reference on pre-Lie-Rinehart algebra (or left-symmetric Rinehart algebra). See [2] for more details |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.geomphys.2022.104501 |
| URL الوصول: | http://arxiv.org/abs/2110.14857 |
| رقم الانضمام: | edsarx.2110.14857 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.geomphys.2022.104501 |
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