Journals / Turkish Journal of Mathematics / 2007 / Cilt: 31 - Sayı: 3

Braiding for Categorical and Crossed Lie Algebras and Simplicial Lie Algebras

Pages
239–255
Publication Date
2007-03-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this work, we give the notion of braiding for categorical Lie algebras and crossed modules of Lie algebras and we give an equivalence between them.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we give the notion of braiding for categorical Lie algebras and crossed modules of Lie algebras and we give an equivalence between them.
📊
Key Findings & Data:In this work, we give the notion of braiding for categorical Lie algebras and crossed modules of Lie algebras and we give an equivalence between them.
💡
Conclusion & Impact:In this work, we give the notion of braiding for categorical Lie algebras and crossed modules of Lie algebras and we give an equivalence between them.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Simplicial Lie Algebra · Categorical Lie Algebra Crossed Modul · Simplicial Lie Algebra

Abstract

In this work, we give the notion of braiding for categorical Lie algebras and crossed modules of Lie algebras and we give an equivalence between them.

Özet

In this work, we give the notion of braiding for categorical Lie algebras and crossed modules of Lie algebras and we give an equivalence between them.

🔖

Cite This Article

ULUALAN, E. (2007). Braiding for Categorical and Crossed Lie Algebras and Simplicial Lie Algebras. Turkish Journal of Mathematics, Cilt: 31 - Sayı: 3, 239–255. https://ajindex.com/articles/723390

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (19)

  1. Ak¸ca, I., Arvasi, Z.: Simplicial and Crossed Lie Algebras. Homology, Homotopy and Appli- cations, 4, (1), 43-57 (2002).
  2. Arvasi, Z., Porter, T.: Higher Dimensional Peiffer Elements in Simplicial Commutative Algebras. Theory and Applications of Categories, 3, (1), 1-23 (1997).
  3. Berger, C.: Double Loop Spaces, Braided Monoidal Categoriesand Algebraic 3-Typesof Spaces. Contemporary Mathematics, 227, 46-66 (1999).
  4. Brown, R., Gilbert, N.D.: Algebraic Modelsof 3-Typesand Automorphism Structuresfor Crossed Modules. Proc. London Math.Soc. (3), 59, 51-73 (1989).
  5. Carrasco, P., Cegarra, A.M.: Group-Theoretic Algebraic Models for Homotopy Types. Jour. Pure Appl. Algebra, 75, 195-235 (1991). Conduch´e, D.: ModulesCrois´ esG´ en´eralis´esde Longueur 2. Jour. Pure Appl. Algebra, 34, 178 (1984).
  6. Curtis, E.B.: Simplicial Homotopy Theory. Adv. in Math., 6, 107-209 (1971).
  7. Duskin, J.: Simplicials Methods and the Interpretation of Triple cohomology. Memoirs A.M.S. 3, 163 (1975).
  8. Ellis, G.J.: Crossed Modules and Their Higher Dimensional Analogues. Ph.D. Thesis, U.C.N.W., (1984).
  9. Ellis, G.J.: Higher Dimensional Crossed Modules of Algebras. Jour. Pure. Appl. Algebra,, 277-282, (1988).
  10. Ellis, G.J.: Homotopical Aspects of Lie Algebras. Jour. Austral. Math. Soc. (Sreies A), 54, 419 (1993).
  11. Garzon, A.R., Miranda, J.G.: Homotopy Theory for (Braided) Cat-Groups. Chaiers de Topologie Geometrie Differentielle Categoriques Vol: XXXVIII-2, (1997).
  12. Joyal, A., Street, R.: Braided Monoidal Categories. Macquarie Mathematics Report 860081, Macquarie University, (1986).
  13. Joyal, A., Street, R.: Braided Tensor Categories. Advances in Math, (1), 82, 20-78 (1991).
  14. Kassel, C., Loday, J.L.: Extensions Centrales d’alg´ebresde Lie. Ann. Ist. Fourier (Greno- ble), 33, 119-142 (1982).
  15. Kamps, K.H., Porter, T.: 2-Groupoids Enrichments in Homotopy Theory and Algebra. K-Theory, 25, 373-409 (2002).
  16. Mutlu, A., Porter, T.: Applicationsof Peiffer Pairingsin the Moore Complex of a Simplicial Group. Theory and Applications of Categories, 4, (7), 148-173 (1998).
  17. Porter, T.: Homology of Commutative Algebras and an Invariant of Simis and Vasconceles. Journal of Algebra, 99, 458-465 (1986).
  18. Whitehead, J.H.C.: Combinatorial Homotopy I and II. Bull. Amer. Math. Soc. 55, 231-245 and 453-496 (1949).
  19. Erdal ULUALAN Dumlupınar University, Department of Mathematics, K¨utahya-TURKEY e-mail: [email protected]