Weak Hopf algebras corresponding to quantum algebras U q (f (K, H))

Aizawa N., Isaac P.S.: Weak Hopf algebras corresponding to Uq[sln]. J. Math. Phys. 44, 5250–5267 (2003)

Bergman G.: The diamond lemma for ring theory. Adv. Math. 29(2), 178–218 (1978)

Block R.E.: The irreducible representations of the Lie algebra sl(2) and of theWeyl algebra. Adv. Math. 39, 69–110 (1981)

Böhm G., Korinél S.: A coassociative C*-quantum group with nonintegral dimensions. Lett. Math. Phys. 38(4), 437–456 (1996)

Böhm G., Nill F., Korinél S.: Weak Hopf algebras I. Integral theory and C* structure. J. Algebra 221, 385–438 (1999)

Drinfeld, V.G.: Quantum groups. In: Proc. Int. Cong. Math. (Berkeley, 1986), pp. 798–820. Amer. Math. Soc., Providence (1987)

Duplij S., Sinelshchikov S.: Quantum enveloping algebras with von Neumann regular Cartanlike generators and the Pierce decomposition. Comm. Math. Phys. 287, 769–785 (2009)

Green J.A., Nicols W.D., Taft E.J.: Left Hopf algebras. J. Algebra 65, 399–411 (1980)

Hayashi T.: Quantum group symmetry of partition functions of IRF models and its application to Jones’ index theory. Commun. Math. Phys. 157(2), 331–345 (1993)

Ji Q.Z., Wang D.G.: Finite-dimensional representations of quantum groups Uq(f(K)). East-West J. Math. 2(2), 201–213 (2000)

Jimbo M.: A q-difference analogue of U(g) and the Yang-Baxter equation. Lett. Math. Phys. 10, 63–69 (1985)

Kassel C.: Quantum Groups. Springer, New York (1995)

Li F.: Weak Hopf algebras and some new solutions of the quantum Yang-Baxter equation. J. Algebra 208, 72–100 (1998)

Li F.: Weak Hopf algebras and regular monoids. J. Math. Res. Exposition 19, 325–331 (1999)

Li F., Duplij S.: Weak Hopf algebras and singular solutions of quantum Yang-Baxter equation. Commun. Math. Phys. 225, 191–217 (2002)

Madore J.: Introduction toNoncommutative Geometry and its Applications. Cambridge University Press, Cambridge (1995)

Montgomery, S.: Hopf Algebras and Their Action on Rings. CBMS, Lecture in Math., vol. 82. AMS, Providence (1993)

Ocneanu, A.: Quantized groups, string algebras and Galois theory for algebras. In: Operator Algebras and Applications, vol. 2, pp. 119–172. London Math. Soc. Lecture Note Ser., 136. Cambridge University Press, Cambridge (1988)

Ringel C.M.: Tame Algebras and Integral Quadratic Forms. LNM 1099. Springer, Berlin (1984)

Sweedler M.E.: Hopf Algebras. Benjamin, New York (1969)

Wang D.G., Ji Q.Z., Yang S.L.: Finite-dimensional representations of quantum groups Uq(f(K)). Commun. Algebra 30, 2191–2211 (2002)

Wu Z.X.: A class of weak Hopf algebras related to a Borcherds-Cartan matrix. J. Phys. A. 39, 14611–14626 (2006)

Yang, S.L.: Weak Hopf algebras corresponding to Cartan matrices. J. Math. Phys. 46(7), Article ID 073502 (2005)

Ye L.X.; Li, F.: Weak quantum Borcherds superalgebras and their representations. J. Math. Phys. 48, Article ID 023502 (2007)