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

last update 2025.6.20

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Hiroyuki Yamane,

Professor,

Department of Mathematics,
Faculty of Science,
Academic Assembly,
University of Toyama,
3190 Gofuku, Toyama-shi, Toyama 930-8555, JAPAN

My presentation in Sao Paulo on 11 August 2018
here

My Note: Yamane, H., Direct definition of formal power series algebra
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
misprints20180914 mispri20250220a

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

Publications:

[Y89a] 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.

[Y89b] H.Yamane, Irreducible projective modules of the Hecke algebras of a finite Coxeter group. J. Algebra 127 (1989), no. 2, 373-384.

[Y92] 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.

[OY90]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.

[Y94] 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.

[Y99] 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.

[Y01] 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.

[Y03] 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.

[Y04] 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.

[Y07] Yamane, H., Representations of a Z/3Z-quantum group, Publ. RIMS, Kyoto Univ., 43 (2007), 75-93.

[HY08] I. Heckenberger, H. Yamane, A generalization of Coxeter groups, root systems, and Matsumoto's theorem, Math. Z.,259 (2008), 255-276, math.QA/0610823

[HSTY08] 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

[Y09] 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

[HY10] Istvan Heckenberger and Hiroyuki Yamane, Drinfel'd doubles and Shapovalov determinants, Revista de la Union Matematica Argentina, Volumen 51, no 2 (2010), 107-146.

[AYY10] 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.

[AAY11] Nicolas Andruskiewitsch, Ivan Angiono, and Hiroyuki Yamane, On pointed Hopf superalgebras, Contemporary Mathematics Vol.544, (2011) 123-140

[AYY12a] Saeid Azam, Hiroyuki Yamane, Malihe Yousofzadeh, Reflectable bases for affine reflection systems, Journal of Algebra 371 (2012) 63-93

[AYY12b] Saeid Azam, Hiroyuki Yamane, Malihe Yousofzadeh, An exposition of root systems and Lie algebras (affine and elliptic), RIMS Kokyuroku Bessatsu, B36 (2012), 17-42

[Y14] 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,

[AY15] Ivan Angiono, Hiroyuki Yamane, The R-matrix of quantum doubles of Nichols algebras of diagonal type, J. Math. Phys. 56, 021702 (2015)

[AYY15] 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.

[Y16] 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

[BY15] Punita Batra and Hiroyuki Yamane, Skew centers of rank-one generalized quantum groups, Toyama Mathematical Journal, Volume 37 (2015), 189-202

[BY18] Punita Batra, Hiroyuki Yamane, Centers of Generalized Quantum Groups, J. Pure Appl. Algebra 222 (2018), no. 5, 1203-1241

[AY18] Ivan Angiono, Hiroyuki Yamane, Bruhat order and nil-Hecke algebras for Weyl groupoids, J. Algebra Appl. 17 (2018), no. 9, 1850166, 17 pp.

[KMY18] 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.

[Y19] 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

[BY20] Punita Batra, Hiroyuki Yamane, Natural Elements of Center of Generalized Quantum Groups, 19-31, Contemp. Math., 751, Amer. Math. Soc., Providence, RI, 2020.

[Y21] Hiroyuki Yamane, Typical Irreducible Characters of Generalized Quantum Groups, J. Algebra Appl. 20 (2021), no. 1, 2140014, 58 pp.

[Y22] Hiroyuki Yamane, Hamilton circuits of Cayley graphs of Weyl groupoids of generalized quantum groups, Toyama. Math. J. 43 (2022), 1-76 Click-here(For English, click 日本語 on the first line)

[LYZ24] Hongda Lin, Hiroyuki Yamane and Honglian Zhang, On generators and defining relations of quantum affine superalgebra U_q({\hat {sl}_{m|n}), J. Algebra Appl. (2024) 2450021 (29 pages)

[IY26] Takato Inoue, Hiroyuki Yamane, Hamiltonian Cycles for Finite Weyl Groupoids, J. Algebra Appl. (2026), 2650054, 40 pp. (onlined)

Cor0909

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