Yetter, David N. Quantum groups and representations of monoidal categories. (English) Zbl 0712.17014 Math. Proc. Camb. Philos. Soc. 108, No. 2, 261-290 (1990). Some categorical explanations of the interactions among knot theory, Hopf algebras and quantum groups are given. In section 8, three open questions are proposed. Reviewer: Li Wanglai Cited in 5 ReviewsCited in 134 Documents MSC: 17B37 Quantum groups (quantized enveloping algebras) and related deformations 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 57Q45 Knots and links in high dimensions (PL-topology) (MSC2010) 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 18D10 Monoidal, symmetric monoidal and braided categories (MSC2010) Keywords:monoidal category; knot theory; Hopf algebras; quantum groups PDFBibTeX XMLCite \textit{D. N. Yetter}, Math. Proc. Camb. Philos. Soc. 108, No. 2, 261--290 (1990; Zbl 0712.17014) Full Text: DOI References: [1] Kulish, Zap. Nauchn. Sem. Leningrad Otdel. Mat. Inst. Steklov 95 pp 129– (1980) [2] DOI: 10.1070/RM1986v041n05ABEH003441 · Zbl 0649.16008 · doi:10.1070/RM1986v041n05ABEH003441 [3] DOI: 10.1016/0022-4049(80)90101-2 · Zbl 0447.18005 · doi:10.1016/0022-4049(80)90101-2 [4] DOI: 10.1103/PhysRevLett.19.1312 · Zbl 0152.46301 · doi:10.1103/PhysRevLett.19.1312 [5] DOI: 10.1016/0003-4916(72)90335-1 · Zbl 0236.60070 · doi:10.1016/0003-4916(72)90335-1 [6] Atiyah, Notes on the Oxford seminar on Jones?Witten theory (1988) [7] DOI: 10.1070/RM1979v034n05ABEH003909 · doi:10.1070/RM1979v034n05ABEH003909 [8] DOI: 10.1143/JPSJ.57.1173 · Zbl 0719.57006 · doi:10.1143/JPSJ.57.1173 [9] Sweedler, Hopf Algebras (1969) [10] DOI: 10.1143/JPSJ.57.757 · Zbl 0719.57005 · doi:10.1143/JPSJ.57.757 [11] DOI: 10.1143/JPSJ.56.3464 · Zbl 0719.57004 · doi:10.1143/JPSJ.56.3464 [12] DOI: 10.1143/JPSJ.56.3039 · Zbl 0719.57003 · doi:10.1143/JPSJ.56.3039 [13] Abe, Hopf Algebras (1977) [14] Reidemeister, Knotentheorie (1932) [15] Reidemeister, Knot Theory (1983) [16] Kauffman, Braids 78 (1988) · doi:10.1090/conm/078/975085 [17] Kauffman, Trans. Amer. Math. Soc. [18] Freyd, J. Pure Appl. Algebra [19] DOI: 10.1016/0001-8708(89)90018-2 · Zbl 0679.57003 · doi:10.1016/0001-8708(89)90018-2 [20] DOI: 10.1007/BF01247086 · Zbl 0641.16006 · doi:10.1007/BF01247086 [21] Deligne, Hodge Cycles, Motives and Shimura Varieties 900 (1982) [22] Penrose, Combinatorial Mathematics and its Applications pp 221– (1971) [23] Manin, Quantum groups and non-commutative geometry (1988) · Zbl 0724.17006 [24] Mac Lane, Rice Univ. Stud. 49 pp 28– (1963) [25] Mac Lane, Categories for the Working Mathematician (1971) · doi:10.1007/978-1-4612-9839-7 [26] DOI: 10.1007/BF01406222 · Zbl 0377.55001 · doi:10.1007/BF01406222 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.