On Leibniz algebras with maximal cyclic subalgebras

Vasiliy A. Chupordia; Leonid A. Kurdachenko; Igor Ya. Subbotin

Commentationes Mathematicae Universitatis Carolinae (2022)

  • Volume: 62 63, Issue: 3, page 277-294
  • ISSN: 0010-2628

Abstract

top
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras.

How to cite

top

Chupordia, Vasiliy A., Kurdachenko, Leonid A., and Subbotin, Igor Ya.. "On Leibniz algebras with maximal cyclic subalgebras." Commentationes Mathematicae Universitatis Carolinae 62 63.3 (2022): 277-294. <http://eudml.org/doc/299042>.

@article{Chupordia2022,
abstract = {We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras.},
author = {Chupordia, Vasiliy A., Kurdachenko, Leonid A., Subbotin, Igor Ya.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Leibniz algebra; Lie algebra; ideal; cyclic Leibniz algebra; derivation},
language = {eng},
number = {3},
pages = {277-294},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On Leibniz algebras with maximal cyclic subalgebras},
url = {http://eudml.org/doc/299042},
volume = {62 63},
year = {2022},
}

TY - JOUR
AU - Chupordia, Vasiliy A.
AU - Kurdachenko, Leonid A.
AU - Subbotin, Igor Ya.
TI - On Leibniz algebras with maximal cyclic subalgebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2022
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62 63
IS - 3
SP - 277
EP - 294
AB - We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras.
LA - eng
KW - Leibniz algebra; Lie algebra; ideal; cyclic Leibniz algebra; derivation
UR - http://eudml.org/doc/299042
ER -

References

top
  1. Ayupov Sh., Omirov B., Rakhimov I., Leibniz Algebras: Structure and Classification, CRC Press, Boca Raton, 2020. 
  2. Batten Ray Ch., Combs A., Gin N., Hedges A., Hird J. T., Zack L., 10.1080/00927872.2012.717655, Comm. Algebra 42 (2014), no. 6, 2404–2410. MR3169714DOI10.1080/00927872.2012.717655
  3. Berkovich Ya., Groups of Prime Power Order. Vol. 1, De Gruyter Expositions in Mathematics, 46, Walter de Gruyter GmbH & Co. KG, Berlin, 2008. MR2464640
  4. Bloh A. M., On a generalization of the concept of Lie algebra, Dokl. Akad. Nauk SSSR 165 (1965), 471–473 (Russian). MR0193114
  5. Chupordia V. A., Kurdachenko L. A., Semko N. N., 10.15407/dopovidi2020.07.017, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki (2020), no. 7, 17–21. MR4169625DOI10.15407/dopovidi2020.07.017
  6. Chupordia V. A., Kurdachenko L. A., Subbotin I. Ya., 10.1142/S0219498817500827, J. Algebra Appl. 16 (2017), no. 5, 1750082, 16 pages. MR3634087DOI10.1142/S0219498817500827
  7. Kirichenko V. V., Kurdachenko L. A., Pypka A. A., Subbotin I. Ya., Some aspects of Leibniz algebra theory, Algebra Discrete Math. 24 (2017), no. 1, 1–33. MR3711054
  8. Kurdachenko L. A., Otal J., Pypka A. A., 10.1007/s40879-016-0093-5, Eur. J. Math. 2 (2016), no. 2, 565–577. MR3499000DOI10.1007/s40879-016-0093-5
  9. Kurdachenko L. A., Otal J., Subbotin I. Ya., On some properties of the upper central series in Leibniz algebras, Comment. Math. Univ. Carolin. 60 (2019), no. 2, 161–175. MR3982464
  10. Kurdachenko L. A., Semko N. N., Subbotin I. Ya., 10.1515/math-2017-0010, Open Math. 15 (2017), no. 1, 92–100. MR3613335DOI10.1515/math-2017-0010
  11. Kurdachenko L. A., Semko N. N., Subbotin I. Ya., On the anticommutativity in Leibniz algebras, Algebra Discrete Math. 26 (2018), no. 1, 97–109. MR3877183
  12. Kurdachenko L. A., Semko N. N., Subbotin I. Ya., Applying group theory philosophy to Leibniz algebras: some new developments, Adv. Group Theory Appl. 9 (2020), 71–121. MR4123458
  13. Kurdachenko L. A., Subbotin I. Ya., Semko N. N., From groups to Leibniz algebras: common approaches, parallel results, Adv. Group Theory Appl. 5 (2018), 1–31. MR3824446
  14. Kurdachenko L. A., Subbotin I. Ya., Yashchuk V. S., Leibniz algebras whose subideals are ideals, J. Algebra Appl. 17 (2018), no. 8, 1850151, 15 pages. MR3825312
  15. Kurdachenko L. A., Subbotin I. Ya., Yashchuk V. S., Leibniz algebras whose subalgebras are left ideals, Serdica Math. J. 46 (2020), no. 2, 175–194. MR4154030
  16. Kurdachenko L. A., Subbotin I. Ya., Yashchuk V. S., 10.1142/S0219498820501133, J. Algebra Appl. 19 (2020), no. 6, 2050113, 14 pages. MR4120090DOI10.1142/S0219498820501133
  17. Loday J.-L., Cyclic Homology, Grundlehren der mathematischen Wissenschaften, 301, Springer, Berlin, 1992. MR1217970
  18. Loday J.-L., Une version non commutative des algèbres de Lie: les algèbres de Leibniz, Enseign. Math. (2) 39 (1993), no. 3–4, 269–293 (French). Zbl0806.55009MR1252069
  19. Loday J.-L., Pirashvili T., 10.1007/BF01445099, Math. Ann. 296 (1993), no. 1, 139–158. Zbl0821.17022MR1213376DOI10.1007/BF01445099
  20. Yashchuk V. S., On some Leibniz algebras, having small dimension, Algebra Discrete Math. 27 (2019), no. 2, 292–308. MR3982309

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.