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JOURNALS // Funktsional'nyi Analiz i ego Prilozheniya

Funktsional. Anal. i Prilozhen., 2007, Volume 41, Issue 2, Pages 24–43 (Mi faa2857)

Krein Duality, Positive 2-Algebras, and Dilation of Comultiplications
A. M. Vershik

References

1. N. Burbaki, Topologicheskie vektornye prostranstva, IL, M., 1959
2. E. Bannai, E. Ito, Algebraicheskaya kombinatorika. Skhemy otnoshenii, Mir, M., 1987  mathscinet
3. V. M. Bukhshtaber, A. M. Vershik, S. A. Evdokimov, I. N. Ponomarenko, “Kombinatornye algebry i mnogoznachnye involyutivnye gruppy”, Funkts. analiz i ego pril., 30:3 (1996), 12–18  mathnet  crossref  mathscinet
4. L. Vainerman, “O rabotakh M. G. Kreina po teorii predstavlenii i garmonicheskomu analizu na topologicheskikh gruppakh”, Ukr. matem. zh., 46:3 (1994), 198–211  mathscinet  zmath
5. A. M. Vershik, “Geometricheskaya teoriya sostoyanii, granitsa fon Neimana, dvoistvennost $C^*$-algebr”, Zap. nauchn. semin. LOMI, 29 (1972), 147–154  mathnet  zmath
6. A. M. Vershik, S. A. Evdokimov, I. N. Ponomarenko, “Algebry v plansherelevoi dvoistvennosti i algebraicheskaya kombinatorika”, Funkts. analiz i ego pril., 31:4 (1997), 34–46  mathnet  crossref  mathscinet  zmath
7. S. A. Evdokimov, Shurovost i otdelimost assotsiativnykh skhem, Diss. d.f.-m.n., SPbGU, 2005
8. K. Kassel, Kvantovye gruppy, Fazis, M., 1999
9. S. V. Kerov, “Dvoistvennost konechnomernykh algebr”, Vestnik LGU, ser matem., 1974, no. 7, 23–29  mathscinet  zmath
10. S. V. Kerov, Dvoistvennost $C^*$-algebr i ee primery v teorii predstavlenii grupp, Diss. k.f.-m.n., LGU, 1974
11. A. Klifford, D. Preston, Algebraicheskaya teoriya polugrupp, 1, Mir, M., 1972  zmath
12. A. N. Kolmogorov, Sobranie sochinenii, 3, 2003  mathscinet
13. M. G. Krein, “O polozhitelnykh funktsionalakh na pochti periodicheskikh funktsiyakh”, Dokl. AN SSSR, 30:1 (1941), 9–12  mathscinet  zmath
14. M. G. Krein, “Printsip dvoistvennosti dlya bikompaktnoi gruppy i kvadratnoi blok-algebry”, Dokl. AN SSSR, 69:6 (1949), 725–728  mathscinet  zmath
15. M. G. Krein, “Ermitovo-polozhitelnye yadra na odnorodnykh prostranstvakh, chast 1”, Ukr. matem. zh., 1:4 (1949), 64–98  mathscinet  zmath
16. M. G. Krein, “Ermitovo-polozhitelnye yadra na odnorodnykh prostranstvakh, chast 2”, Ukr. matem. zh., 2:1 (1950), 10–59  mathscinet  zmath
17. V. A. Oganesyan, “O poluprostote sistemnoi algebry”, Dokl. AN Arm. SSR, 21 (1955), 145–147  mathscinet  zmath
18. B. Sekefalvi-Nad, Ch. Foyash, Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970  mathscinet
19. S. Bochner, “On a theorem of Tannaka and Krein”, Ann. of Math., 43 (1942), 56–58  crossref  mathscinet  zmath
20. G. I. Olshansky, “Unitary representations of the infinite symmetric group: a semigroup approach”, Representation of Lie groups and Lie algebras, Akad. Kiado, Budapest, 1985, 181–197.  mathscinet
21. V. M. Buchstaber, “$n$-valued groups: theory and applications”, Moscow Math. J., 6:1 (2006), 57–84  mathnet  crossref  mathscinet  zmath
22. P. Deligne, “Catégories tannakiennes”, Progr. Math., 87, Birkhäuser, Boston, MA, 1990, 111–195  mathscinet  zmath
23. A. Joyal, R. Street, “An introduction to Tannaka duality and quantum groups”, Lecture Notes in Math., 1448, Springer-Verlag, Berlin, 1991, 413–492  crossref  mathscinet
24. D. G. Higman, “Invariant relations, coherent configurations, generalized polygons”, Combinatorics (Proc. Advanced Study Inst., Breukelen, 1974), Part 3: Combinatorial Group Theory, Math. Centre Tracts, No. 57, Math. Centrum, Amsterdam, 1974, 27–43  mathscinet  zmath
25. A. Massoud, Tannaka–Krein duality for compact groups, http://arxiv.org/abs/math/0308259
26. N. Saavedra Rivano, Catégories tannakienns, Lecture Notes in Math., 265, Springer-Verlag, Berlin–New York, 1972  mathscinet  zmath
27. L. Scott, “A condition on Higman parameters”, Notices Amer. Math. Soc., 701 (1972), 20–45
28. L. Scott, “Modular permutation representations”, Trans. Amer. Math. Soc., 175 (1973), 101–121  crossref  mathscinet  zmath
29. T. Tannaka, “Über den Dualitätssatz der nichtkommutativen topologishen Gruppen”, Tohoku Math. J., 45 (1938), 1–12  zmath
30. A. Van Daele, “Quantum groups with invariant integrals”, Proc. Nat. Acad. Sci. USA, 97:2 (2000), 541–546  crossref  mathscinet  zmath  adsnasa  scopus
31. A. Vershik, “Polymorphisms, Markov processes, and quasi-similarity”, Discrete Contin. Dyn. Syst., 13:5 (2005), 1305–1324  crossref  mathscinet  zmath  elib  scopus
32. A. Vershik, Dvoistvennost Kreina, pozitivnye 2-algebry i dilatatsiya koumnozhenii, Preprint POMI №1, 2007


© Steklov Math. Inst. of RAS, 2026