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ЖУРНАЛЫ // Алгебра и анализ

Алгебра и анализ, 2008, том 20, выпуск 2, страницы 70–133 (Mi aa506)

Теория представлений алгебры (модифицированного) уравнения отражений $GL(m|n)$ типа
Д. И. Гуревич, П. Н. Пятов, П. А. Сапонов

Эта публикация цитируется в следующих статьяx:
  1. Victor Bovdi, Andriy Panasyuk, Vsevolod Shevchishin, “On linear-quadratic Poisson pencils on trivial central extensions of semisimple Lie algebras”, Anal.Math.Phys., 16:1 (2026)  crossref
  2. Dimitry Gurevich, Pavel Saponov, Mikhail Zaitsev, “Representations of Spectrum of GL(m) type Quantum Matrices”, Journal of Geometry and Physics, 2026, 105995  crossref
  3. Dimitry Gurevich, Pavel Saponov, “Generalized Harish-Chandra morphism on Reflection Equation algebras”, Journal of Geometry and Physics, 210 (2025), 105435  crossref
  4. Dmitry V. Talalaev, “RE-algebras, quasi-determinants and the full Toda system”, Partial Differential Equations in Applied Mathematics, 11 (2024), 100898  crossref
  5. Д. И. Гуревич, П. А. Сапонов, В. В. Соколов, “О симметризаторах в квантовых матричных алгебрах”, УМН, 78:4(472) (2023), 203–204  mathnet  crossref  mathscinet  zmath  adsnasa; D. I. Gurevich, P. A. Saponov, V. V. Sokolov, “On symmetrizers in quantum matrix algebras”, Russian Math. Surveys, 78:4 (2023), 785–787  crossref  isi
  6. Dimitry Gurevich, Pavel Saponov, Contemporary Mathematics, 789, The Diverse World of PDEs, 2023, 101  crossref
  7. Slaven Kožić, “On the h-adic Quantum Vertex Algebras Associated with Hecke Symmetries”, Commun. Math. Phys., 397:2 (2023), 607  crossref
  8. Dimitry Gurevich, Pavel Saponov, “Noncommutative geometry on central extension of U(u(2))”, Journal of Mathematical Physics, 64:6 (2023)  crossref
  9. Gurevich D., Saponov P., “Quantum Doubles of Fock Type and Bosonization”, J. Geom. Phys., 171 (2022), 104396  crossref  mathscinet  isi
  10. Д. И. Гуревич, П. А. Сапонов, “Детерминанты в квантовых матричных алгебрах и интегрируемые системы”, ТМФ, 207:2 (2021), 261–276  mathnet  crossref  mathscinet  adsnasa; D. I. Gurevich, P. A. Saponov, “Determinants in quantum matrix algebras and integrable systems”, Theoret. and Math. Phys., 207:2 (2021), 626–639  crossref  isi
  11. Gurevich D., Saponov P., “Doubles of Associative Algebras and Their Applications”, Phys. Part. Nuclei Lett., 17:5 (2020), 774–778  crossref  isi  scopus
  12. Gurevich D., Saponov P., Slinkin A., “Bethe Subalgebras in Braided Yangians and Gaudin-Type Models”, Commun. Math. Phys., 374:2 (2020), 689–704  crossref  mathscinet  isi  scopus
  13. Gurevich D., Saponov P., “Braided Yangians”, J. Geom. Phys., 138 (2019), 124–143  crossref  mathscinet  zmath  isi  scopus
  14. Lechner G., Pennig U., Wood S., “Yang-Baxter Representations of the Infinite Symmetric Group”, Adv. Math., 355 (2019), 106769  crossref  mathscinet  isi
  15. Gurevich D. Saponov P. Talalaev D., “Drinfeld-Sokolov Reduction in Quantum Algebras: Canonical Form of Generating Matrices”, Lett. Math. Phys., 108:10 (2018), 2303–2314  crossref  mathscinet  isi  scopus
  16. Д. И. Гуревич, П. А. Сапонов, “Обобщенные янгианы и их пуассонова структура”, ТМФ, 192:3 (2017), 351–368  mathnet  crossref  mathscinet  adsnasa  elib; D. I. Gurevich, P. A. Saponov, “Generalized Yangians and their Poisson counterparts”, Theoret. and Math. Phys., 192:3 (2017), 1243–1257  crossref  isi
  17. Gurevich D., Saponov P., “Derivatives in noncommutative calculus and deformation property of quantum algebras”, J. Noncommutative Geom., 10:4 (2016), 1215–1241  crossref  mathscinet  zmath  isi  scopus
  18. Gurevich D., Rubtsov V., Saponov P., Skoda Z., “Generalizations of Poisson Structures Related To Rational Gaudin Model”, Ann. Henri Poincare, 16:7 (2015), 1689–1707  crossref  mathscinet  zmath  isi  elib  scopus
  19. Gurevich D., Saponov P., “Braided Algebras and their Applications to Noncommutative Geometry”, Adv. Appl. Math., 51:2 (2013), 228–253  crossref  mathscinet  zmath  isi  elib  scopus
  20. Gurevich D. Pyatov P. Saponov P., “Braided Weyl algebras and differential calculus on $U(u(2))$”, J. Geom. Phys., 62:5 (2012), 1175–1188  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  21. Ruuge A.E., Van Oystaeyen F., “Distortion of the Poisson bracket by the noncommutative Planck constants”, Comm. Math. Phys., 304:2 (2011), 369–393  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  22. Gurevich D., Pyatov P., Saponov P., “Braided differential operators on quantum algebras”, J. Geom. Phys., 61:8 (2011), 1485–1501  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  23. Gurevich D., Saponov P., “Generic super-orbits in $\mathrm{gl}(m|n)^*$ and their braided counterparts”, J. Geom. Phys., 60:10 (2010), 1411–1423  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  24. Gurevich D., Saponov P., “Wave operators on quantum algebras via noncanonical quantization”, Acta Appl. Math., 109:1 (2010), 19–38  crossref  mathscinet  zmath  isi  elib  scopus
  25. Д. И. Гуревич, П. Н. Пятов, П. А. Сапонов, “Спектральная параметризация для степенных сумм квантовых суперматриц”, ТМФ, 159:2 (2009), 207–219  mathnet  crossref  mathscinet  zmath  adsnasa; D. I. Gurevich, P. N. Pyatov, P. A. Saponov, “Spectral parameterization for power sums of a quantum supermatrix”, Theoret. and Math. Phys., 159:2 (2009), 587–597  crossref  isi
  26. Gurevich D., Saponov P., “Braided affine geometry and $q$-analogs of wave operators”, J. Phys. A, 42:31 (2009), 313001, 51 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  27. Roubtsov V., Skrypnyk T., “Compatible Poisson brackets, quadratic Poisson algebras and classical $r$-matrices”, Differential equations: geometry, symmetries and integrability, Abel Symp., 5, Springer, Berlin, 2009, 311–333  mathscinet  zmath  isi
  28. Dutriaux A., Gurevich D., “The Maxwell operator on $q$-Minkowski space and $q$-hyperboloid algebras”, J. Phys. A, 41:31 (2008), 315203, 19 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  29. Dimitri Gurevich, Pavel Pyatov, Pavel Saponov, “Reflection equation algebra in braided geometry”, J. Gen. Lie Theory Appl., 2:3 (2008), 162  crossref
  30. Antoine Dutriaux, Dimitri Gurevich, “Noncommutative Dynamical Models with Quantum Symmetries”, Acta Appl Math, 101:1-3 (2008), 85  crossref


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