* Welcome to Hiroyuki Yamane's Homepage in University of Toyama

last update 2019.4.1


Hiroyuki Yamane,


Department of Mathematics,
Faculty of Science,
University of Toyama,
Gofuku, Toyama 930-8555, JAPAN

My presentation in Sao Paulo on 11 August 2018

the pdf-file

the pdf-file

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2016年度の代数学IIのTheorem 15について
the pdf-file


My Note: Yamane, H., Relations of small rank affine superalgebras
the pdf-file

Yamane, H., A direct proof of of Commutation relations of Uq sl(2)^(1)
the pdf-file

Hiroyuki Yamane, Note of a proof of Matsumoto's theorem of (non-crystallographic) Coxeter groups,
the pdf-file (2017-6-9)


H.Yamane, A Poincare-Birkhoff-Witt theorem for quantized universal enveloping algebras of type A_N. Publ. Res. Inst. Math. Sci. 25 (1989), no. 3, 503-520.

H.Yamane, Irreducible projective modules of the Hecke algebras of a finite Coxeter group. J. Algebra 127 (1989), no. 2, 373-384.

H.Yamane, On representation theories of Iwahori-Hecke algebras H q (W)  at roots q  of unity (in particular, explicit formulas on H_{primitive n-th root of 1}(S_n) and H_{primitive n-1-th root of 1}(S_n), Quantum groups, integrable statistical models and knot theory (Tianjin, 1992), 319–342, Nankai Lecture Math. Phys., World Sci. Publ.

M.Okado, H.Yamane, R  -matrices with gauge parameters and multi-parameter quantized enveloping algebras. Special functions (Okayama, 1990), 289–293, ICM-90, Satell. Conf. Proc., Springer, Tokyo, 1991.

H.Yamane, Quantized enveloping algebras associated with simple Lie superalgebras and their universal R-matrices. Publ. Res. Inst. Math. Sci. 30 (1994), no. 3, 15-87.

H.Yamane, On defining relations of affine Lie superalgebras and affine quantized universal enveloping superalgebras. Publ. Res. Inst. Math. Sci. 35 (1999), no. 3, 321-390.

H.Yamane, Errata to: ??On defining relations of affine Lie superalgebras and affine quantized universal enveloping superalgebras, Publ. Res. Inst. Math. Sci. 37 (2001), no. 4, 615-619.

H.Yamane, A central extension of U_q sl(2|2)^(1) and R-matrices with a new parameter, J. Math. Phys. 44 (2003), no. 11, 5450-5455.

H.Yamane, A Serre-type theorem for the elliptic Lie algebras with rank geq2. Publ. Res. Inst. Math. Sci. 40 (2004), no. 2, 441-469.

Yamane, H., Representations of a Z/3Z-quantum group, Publ. RIMS, Kyoto Univ., 43 (2007), 75-93.

I. Heckenberger, H. Yamane, A generalization of Coxeter groups, root systems, and Matsumoto's theorem, Mathematishe Zeitschrift, 259 (2008), 255-276, math.QA/0610823

I. Heckenberger, F. Spill, A. Torrielli, H. Yamane, Drinfeld second realization of the quantum affine superalgebras of D^(1)(2,1;x) via the Weyl groupoid. RIMS Kokyuroku Bessatsu B8 (2008), 171-216. (refereed under the editors Toshiyuki Tanisaki, Takeshi Suzuki), arXiv:0705.1071

H.Yamane, Iwahori-Hecke type algebras associated with Lie superalgebras A(m,n), B(m,n), C(n) and D(m,n). RIMS Kokyuroku Bessatsu B11 (2009), 197-222. (refereed under the editors Susumu Ariki, Masato Okado), arXiv:0810.5386

Istvan Heckenberger and Hiroyuki Yamane, Drinfel'd doubles and Shapovalov determinants, Revista de la Union Matematica Argentina, Volumen 51, no 2 (2010), 107-146.

Saeid Azam, Hiroyuki Yamane and Malihe Yousofzadeh , A Finite Presentation of Universal Coverings of Lie Tori, Publications of the Research Institute for Mathematical Sciences, Volume 46, Issue 3 (2010), 507-548.

Nicolas Andruskiewitsch, Ivan Angiono, and Hiroyuki Yamane, On pointed Hopf superalgebras, Contemporary Mathematics Vol.544, (2011) 123-140

Saeid Azam, Hiroyuki Yamane, Malihe Yousofzadeh, Reflectable bases for affine reflection systems, Journal of Algebra 371 (2012) 63-93

Saeid Azam, Hiroyuki Yamane, Malihe Yousofzadeh, An exposition of root systems and Lie algebras (affine and elliptic), RIMS Kokyuroku Bessatsu, B36 (2012), 17-42

Hiroyuki Yamane, Exposition on classification of finite dimensional irreducible representations of the Lie superalgebra B (m, n), XXII International Conference on Integrable Systems and Quantum Symmetries (ISQS-22), Journal of Physics: Conference Series 563 (2014) 012035 doi:10.1088/1742-6596/563/1/012035,

Ivan Angiono, Hiroyuki Yamane, The R-matrix of quantum doubles of Nichols algebras of diagonal type, J. Math. Phys. 56, 021702 (2015)

Saeid Azam, Hiroyuki Yamane, Malihe Yousofzadeh, Classification of Finite Dimensional Irreducible Representations of Generalized Quantum Groups via Weyl Groupoids, Publ. Res. Inst. Math. Sci. 51 (2015), no. 1, 59-130.

Hiroyuki Yamane, Generalized root systems and the affine Lie superalgebra ${\mathrm{G}}^{(1)}(3)$, São Paulo Journal of Mathematical Sciences, (September 09 2015) DOI 10.1007/s40863-015-0021-5, June 2016, Volume 10, Issue 1, pp 9-19

Punita Batra and Hiroyuki Yamane, Skew centers of rank-one generalized quantum groups, Toyama Mathematical Journal, Volume 37 (2015), 189-202

Punita Batra, Hiroyuki Yamane, Centers of Generalized Quantum Groups, J. Pure Appl. Algebra 222 (2018), no. 5, 1203-1241

Ivan Angiono, Hiroyuki Yamane, Bruhat order and nil-Hecke algebras for Weyl groupoids, J. Algebra Appl. 17 (2018), no. 9, 1850166, 17 pp.

Naihuan Jing, Kailash Misra, Hiroyuki Yamane, Kostant-Lusztig \mathbb{A}-bases of Multiparameter Quantum Groups, Representations of Lie algebras, quantum groups and related topics, 149-164, Contemp. Math., 713, Amer. Math. Soc., Providence, RI, 2018.

Hiroyuki Yamane, Lowest positive almost central elements of U_q(sl^{(1)}(n|n)) (n\geq 2), U_q(sl^{(2)}(2n|2n)) (n\geq 2) and U_q(sl^{(4)}(2n+1|2n+1)) (n\geq 1) and their multi-parameter quantum affine superalgebras, in `Proceedings of Meeting for Study of Number theory, Hopf algebras and related topics', 2019, pp.125-140, Yokohama Publishers, ISBN 978-4-946552-65-6

My Preprints:

Punita Batra, Hiroyuki Yamane, Natural Elements of Center of Generalized Quantum Groups, to appear