Öz
The parafree Leibniz algebras are a special class of Leibniz algebras which have many properties with a free Leibniz algebra. In this note, we introduce the structure of parafree Leibniz algebras. We survey the
important results in parafree Leibniz algebras which are analogs of corresponding results in parafree Lie algebras. We first investigate some properties of subalgebras and quotient algebras of parafree Leibniz algebras. Then, we describe the direct sum of parafree Leibniz algebras. We show that the direct sum of two parafree Leibniz algebras is a Leibniz algebra. Furthermore, we prove that the direct sum of two parafree Leibniz algebras is again parafree.
Anahtar Kelimeler
Parafree Leibniz algebra subalgebras quotient algebras direct sum
Kaynakça
- 1. Bahturin, Y. Identity relations in Lie algebras, VNU Science Press, Utrecht, 1987.
- 2. Baur, H. 1980. A note on parafree Lie algebras, Commun. in Alg.; 8(10): 953-960.
- 3. Baur, H. 1978. Parafreie Lie algebren and homologie, Diss. Eth Nr.; 6126: 60 pp.
- 4. Bloh, A.M. 1965. A generalization of the concept of Lie algebra, Dokl. Akad. Nauk SSSR; 165: 471-473.
- 5. A.M. Bloh, A.M. 1971. A certain generalization of the concept of Lie algebra, Algebra and Number Theory, Moskow. Gos. Ped. Inst. U`cen; 375: 9-20.
- 6. Ekici, N, Velioğlu, Z. 2014. Unions of Parafree Lie algebras, Algebra; Article ID 385397.
- 7. Ekici, N, Velioğlu, Z. 2015. Direct Limit of Parafree Lie algebras, Journal of Lie Theory; 25(2): 477-484.
- 8. Evans, T. 1969. Finitely presented loops, lattices, etc. are Hopfian, J. London Math. Soc.; 44: 551-552.
- 9. Loday, J.L., Pirashvili, T. 1993. Universal enveloping algebras of Leibniz algebras and (co)homology, Math. Ann.; 269(1): 139-158.
- 10. Velioğlu, Z. 2013. Subalgebras and Quotient algebras of Parafree Lie algebras, I. Journal Pure and Applied Maths.; 83(3) 507-514.
Öz
Kaynakça
- 1. Bahturin, Y. Identity relations in Lie algebras, VNU Science Press, Utrecht, 1987.
- 2. Baur, H. 1980. A note on parafree Lie algebras, Commun. in Alg.; 8(10): 953-960.
- 3. Baur, H. 1978. Parafreie Lie algebren and homologie, Diss. Eth Nr.; 6126: 60 pp.
- 4. Bloh, A.M. 1965. A generalization of the concept of Lie algebra, Dokl. Akad. Nauk SSSR; 165: 471-473.
- 5. A.M. Bloh, A.M. 1971. A certain generalization of the concept of Lie algebra, Algebra and Number Theory, Moskow. Gos. Ped. Inst. U`cen; 375: 9-20.
- 6. Ekici, N, Velioğlu, Z. 2014. Unions of Parafree Lie algebras, Algebra; Article ID 385397.
- 7. Ekici, N, Velioğlu, Z. 2015. Direct Limit of Parafree Lie algebras, Journal of Lie Theory; 25(2): 477-484.
- 8. Evans, T. 1969. Finitely presented loops, lattices, etc. are Hopfian, J. London Math. Soc.; 44: 551-552.
- 9. Loday, J.L., Pirashvili, T. 1993. Universal enveloping algebras of Leibniz algebras and (co)homology, Math. Ann.; 269(1): 139-158.
- 10. Velioğlu, Z. 2013. Subalgebras and Quotient algebras of Parafree Lie algebras, I. Journal Pure and Applied Maths.; 83(3) 507-514.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 29 Eylül 2022 |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 18 Sayı: 3 |
