Drinfel’d associator and relations of some special functions
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Tóm tắt
We observe the differential equation dG(z) / dz = (x0 / z + x1 / (1- z))G(z) in the space of power series of noncommutative indeterminates x0, x1 , where the coefficients of G(z) are holomorphic functions on the simply connected domain ℂ \ [(-∞,0)∪(1,+∞)].Researches on this equation in some conditions turn out different solutions which admit Drinfel'd associator as a bridge. In this paper, we review representations of these solutions by generating series of some special functions such as multiple harmonic sums, multiple polylogarithms and polyzetas. Thereby, relations in explicit forms or asymptotic expansions of these special functions from the bridge equations are deduced by identifying local coordinates.
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Từ khóa
Drinfel'd associator, multiple harmonic sums, multiple polylogarithms, polyzetas, special functions
Tài liệu tham khảo
Chien, B. V., Duchamp, G. H. E., & Hoang, N. M. V. (2013). Schützenberger's factorization on the (completed) Hopf algebra of q-stuffle product. JP Journal of Algebra, Number Theory and Applications, 30, 191-215.
Chien, B. V., Duchamp, G. H. E., & Hoang, N. M. V. (2015). Structure of Polyzetas and Explicit Representation on Transcendence Bases of Shuffle and Stuffle Algebras. P. Symposium on Symbolic and Algebraic Computation, 40, 93-100.
Chien B. V., Duchamp G. H. E., & Hoang, N. M. V. (2015). Computation tool for the q- deformed quasi-shuffle algebras and representations of structure of MZVs. ACM Communications in Computer Algebra, 49, 117-120.
Cristian, C., & Hoang, N. M. V. (2009). Noncommutative algebra, multiple harmonic sums and applications in discrete probability. Journal of Symbolic Computation, 801-817.
Drinfel'd, V. G. (1990). On quasitriangular quasi- Hopf algebras and on a group that. Algebra i Analiz, 2, 149-181.
Hoang, N. M. (2013a). On a conjecture by Pierre Cartier about a group of associators. Acta Mathematica Vietnamica, 38, 339-398.
Hoang, N. M. (2013b). Structure of polyzetas and Lyndon words. Vietnam Journal of Mathematics, 41, 409-450.
Knizhnik, V. G., & Zamolodchikov, A. B. (1984). Current algebra and Wess-Zumino model in two dimensions. Nuclear Physics. B. Theoretical, Phenomenological, and Experimental High Energy Physics. Quantum Field Theory and Statistical Systems, 247, 83-103.
Radford, D. E. (1979). A natural ring basis for the shuffle algebra and an application to group schemes. Journal of Algebra, 58, 432-454.
Ree, R. (1958). Lie elements and an algebra associated with shuffles. Annals of Mathematics. Second Series, 68, 210-220.
Reutenauer, C. (1993). Free Lie algebras. Clarendon Press: The Clarendon Press, Oxford University Press, New York.
Thang, L. T. Q., & Murakami, J. (1996). Kontsevich's integral for the Kauffman polynomial. Nagoya Mathematical Journal, 142, 39-65.