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Full Name
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Lashkhi Alexandr
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| Address | |
| Georgia | |
| Phone | |
| +995 32 2337487 (office); 99 556927 (mobile); 232397 (home) | |
| Fax | |
| +995 32 2365155 | |
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E-mail
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| Web Page | |
| www.rmi.ge/~lashkhi | |
| Date Of Birth | |
| 1945-02-04 | |
| Education | |
| 1962-1968 Faculty of Mathematics, Tbilisi State University 1968 Diploma in Mathematics (with honour), Tbilisi State University, П № 687578 1968-1971 Post graduate student at the Moscow State University, Department of Algebra (Prof. A. G. Kurosh, Head of Dept., Supervisor Prof. A. L. Shmel kin 1973 Ph.D. in Mathematics (Algebra) – VAK USSR, Moscow, 25.05.1973, МФМ № 019954 1989 Doctor Hab. in Mathematics (Geometry) – VAK USSR, Moscow 22.12.1989, ФМ № 005486 | |
| Position | |
| Professor, head of Applied Mathematics and Computer Modelling Department at the Georgian Technical University | |
| Publications | |
| Impact Journals 1. Subrepresentation lattice of Lie algebras. (Russian) Sibirian Math. J. (in print). 2. Lattices of subrepresentations of Lie algebras and their isomorphisms. (Russian) Sibirian Math. J. (in print). 3. Lattice isomorphisms of stable representations of Lie algebras. Sibirian Math. J. (in print). 4. Lattices of subgroups and geometry of W-power groups (with T. Bokelavadze). (Russian) Dokl. Akad. Nauk., Ross. Akad. Nauk 429 (2009), No. 6, 1-4. 5. On the fundamental theorem of geometric algebra over SF-rings (with T. Kvirikashvili). Comm. Algebra 36 (2008), No. 9, 3564-3573. 6. Affine geometry of modules over a ring with invariant basis number (with T. Kvirikashvili). (Russian) Mat. Zametki 82 (2007), No. 6, 838-849; English transl.: Math. Notes 82 (2007), No. 5, 756-765. 7. A projective geometry of Lie Algebras. (Russian) Dokl. Akad. Nauk., Ross. Akad. Nauk 417 (2007), No. 3, 313-315. 8. Coordinatization of PI-geometrical lattices. (Russian) Dokl. Akad. Nauk 409 (2006), No. 2; English transl.: Dokl. Math. 74 (2006), No. 1, 494-497. 9. Perspective maps for modules (with T. G. Kvirikashvili). (Russian) Mat. Zametki 77, (2005), No. 6, 946-947; English transl.: Math. Notes 77 (2005), No. 6, 876-877. 10. On Lie algebras with many nilpotent subalgebras (with I. Zimmermann). Commun. In Algebra 34 (2004), No. 2, 595-600. 11. Harmonic maps over rings. Georgian Math. J. 4 (1997), No. 1, 41-64. 12. Lattices of subalgebras of solvable Lie algebras. Contemp. Math., 131, Part 2, Amer. Math. Soc., Providence, RI, 1992, 69-89. 13. Harmonic maps over rings. (Russian) Mat. Zametki 47 (1990), No. 1, 161-163; English transl.: Math. Notes 47 (1991), 83-85. 14. Modularity and distributivity in the subideal lattice of a Lie algebra (with I. A. M. Zimmermann) Rend. Sem. Mat. Univ. Padova 73 (1985), 169-177. 15. On Lie algebras with modular lattices of subalgebras. J. Algebra 99 (1986), No. 1, 80-88. 16. Projection of pure supersolvable Lie rings. (Russian) Mat. Zametki 26 (1979), No. 6, 931-937; English transl.: Math. Notes. 6 (1979), 970-974. 17. Lattice isomorphisms of rings and Lie algebras. (Russian) Dokl. Akad. Nauk SSSR 228 (1976), No. 3, 537-539; English transl.: Sov. Math., Dokl. 17 (1976), 770-773. Books and monographs 18. (eds.) The Kight in the Panter’s Skin. Meeting with G. Chogoshvili by F. Bauer and Some Memoirs on Chogoshvili, GTU, 2010 (English, Georgian, Russian). 19. Графо-геометрическое моделирование и исследование комплекса чаеподрезочных машин (с совместно Н. А. Габуния). Технический университет, 2010. 20. (eds.) Proceedings of the International Conference Modern Algebra and Its Applications (September 20-26, 2010). Georgian Technical University, 2010. 21. Mathematical Education in Georgia 1801-1951 (with L. Beridze). (Georgian) Georgian Technical University, Tbilisi, 2009. 22. Modeling of ring geometry von Neumann’s point of view. Nova Science Publishers, New York (will appeared, 2009-2010). 23. Lattices of subrepresentations of Lie algebras and their isomorphisms. (Russian) Contemp. Math. Its Appl. 46 (2007), 135-164; English transl.: J. Math. Sci. (N. Y.) 141 (2007), 188-232. 24. Мировозренческие вопросы в теоретических основах прикладной геометрии (совместно с А. Шавгулидзе). Изд. ГТУ, Тбилиси, 2001. 25. Разработка одной интериретации метода проекции с отметками для и . (совместно с А. Шавгулидзе). Изд. ГТУ, Тбилиси, 2001. 26. General geometric lattices and projective geometry of modules. (Russian) VINITI Itogi Nauki i tekniki. Sovrem. Mat. i Prilozh., Geometria 8 (1995), 168-211; English transl.: Geometry, 1. J. Math. Sci. 74 (1995), No. 3, 1044-1077. 27. The fundamental theorem of projective geometry for modules and Lie algebras. (Russian) VINITI Itogi Nauki i tekniki. Sovrem. Mat. i Prilozh., Geometria 18 (1986), 167-187; English transl.: J. Soviet Math. 42 (1988), No. 5, 1991-2007. 28. Lattices with modular identity and Lie algebras. (Russian) VINITI Itogi Nauki i tekniki. Sovrem. Mat. i Prilozh., Moder Mat. and Its Appl. 26 (1985), 213-257; English transl.: J. Soviet Math. 38 (1987), No. 2, 1829-1853. 29. Lie algebras with modular lattices of subalgebras. Mathematisches Institut der Albert-Ludvig-Universität, Freiburg Univ. Pr., Freiburg in Breigau, 1984, pp. 63. 30. (eds.) Proceedings of the International Conference Modern Algebra and Its Applications (September 20-26, 2010). Georgian Technical University, 2011. International Journals 31. Проектирование алгебр Ли. Вестник МГУ, Сер. I (Семинар по алгебре), 1976, № 6, 119-120. 32. Projections of mixed Lie rings. Universal algebra and applications (Warsaw, 1978), 57-66, Banach Center Publ., 9, PWN, Warsaw, 1982. 33. О пректировании сплетений алгебр Ли. Вестник МГУ (Семинар по алгебре), 1980, № 5, 97-98. 34. Projection of wreath products of Lie algebras. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 69 (1980), No. 6, 313-316. 35. L-homomorphisms of Lie algebras. Atti Accademie Nazionale dei Lincei, Roma 70 (1982), No. 2, 6-68. 36. Проектипование рациональных колец Ли. Исследования по алгебре (МГУ и ТГУ), Изд. ТГУ, Тбилиси, 1985, 130-141. 37. Модулярные алгебры Ли. Вестник МГУ (Семинар по алгебре) 1 (1980), 82-83. 38. Решеточная характеризация разрешимых алгебр Ли. Вестник МГУ (семинар по алгебре), 1986, № 6, 103-104. 39. Lattice isomorphisms of certain classes of Lie algebras. (Russian) Collection of Ar¬tic¬les on Algebra, 1. Trudy Mat. Inst. Razmadze 46 (1975), 5-21. 40. Проективная геометрия модулей и алгебр Ли. Вестник МГУ (семинар по ал¬гебре), 1989, № 6, 123-124. 41. Lattices of subalgebras of solvable Lie algebras. Proceedings of the International Conference on Algebra, Part 2 (Novosibirsk, 1989), 1992, 69-89. 42. Geometry of classical groups over rings. Kurosh Algebraic Conference’98, Abstracts of Talks, Moscow, 1998, 76-77. 43. Coset lattices and the fundamental theorem of affine geometry for Lie algebras (with T. Gelashvili). Proc. A. Razmadze Math. Inst. 119 (1999), 43-58. 44. Некоторые приложения теории полезности в задачах моделирования поведе¬ния потрбителей инфокоммуникационных услуг (совместно с П. Гурцкая). Инфор¬ма-ционные технологии, Москва 2 (2003), 43-46. 45. Affine geometry of modules over a ring with an invariant basis number (with T. Kvirikashvili). (Russian) Sovrem. Mat. Prilozh. No. 22, Algebra i Geom. (2004), 126-138; English transl.: J. Math. Sci. (N. Y.) 137 (2006), No. 5, 5161-5173. 46. Ring geometries and their related lattices. (Russian) Fundam. Prikl. Mat. 11 (2005), No. 3, 127-137; English transl.: J. Math. Sci. (N. Y.) 144 (2007), No. 2, 3960-3967. 47. On the fundamental theorem of geometric algebra. International Algebraic Conference in Honor of 250 Universally of Moscow State University, Moscow, 2004, 225-226. 48. Perspective maps of modules (with T. G. Kvirikashvili). (Russian) Contemp. Math. Its Appl. 27 (2004); English transl.: J. Math. Sci. (N. Y.) 139 (2007). 49. Perspective maps over rings (with T. Kvirikashvili). Proc. A. Razmadze Math. Inst. 31 (2003), 139-140. 50. S-minimal non-nilpotent Lie algebras (with I. Zimmermann). Proc. A. Razmadze Math. Inst. 131 (2003), 141-142. 51. Modelling of ring geometry von Neumann’s point of view. Proceedings of the International Conference Modern Algebra and Its Applications, 2010, 104-106. 52. Dezargues, Pappus, Pash configurations in D-semimodular lattices (with P. Gurtskaia). Proceedings of the International Conference Modern Algebra and Its Applications, 2010, 74-78. 53. Geometrical maps in ring affine geometries (with T. Kvirikashvili). Proceedings of the International Conference Modern Algebra and Its Applications, 2010, 93-99. 54. Affine lattices of power groups (with T. Bokelavadze). Proceedings of the International Conference Modern Algebra and Its Applications, vol. 1, 2011, 34-39. 55. Chein conditions in D-semimodular lattices. (with P. Gurtskaia). Proceedings of the International Conference Modern Algebra and Its Applications, vol. 1, 2011, 165-177. 56. Harmonic maps and von Staudt’s theorem over rings (with T. Kvirikashvili). Proceedings of the International Conference Modern Algebra and Its Applications, vol. 2, 2011, 75-84. | |
| Conferences,contacts,other scientific and educational activities | |
| • International Congress of Mathematicians, Berlin, July 15-25, 1998 • Kurosh International Algebraic Conference 98, Moscow, 1998, MSU (Invited Lecture) • International Congress of Mathematicians, Beijing, August 20-28, 2002 (Program Coordinator) • The Conference Modern Algebra and Its Application on the occasion of 70th-anniversary of Academician Kh. Inasaridze, Tbilisi, 2002 (Conference Organizer) • Geometry and Group Theory Methods in Physics and Mathematics, UNESCO International School and Workshop, Batumi, September 15-27, 2003 (Program Coordinator) • UNIESCO International School and Workshop in Honour G. Chogoshvili Algebra, Topology and Geometry, Batumi, 2003 (Conference Organizer) • International Algebraic Conference Dedicated to 250th Anniversary of the Moscow State University, 2004 (Invited Lecture) • International Conference Group Theory and Universal Algebra in Honor of Boris I. Plotkin, December 20-22, 2005, Jerusalem – Beer Sheva (Invited Lecture) • Georgian Mathematical Conferences III and IV Meetings, Tbilisi (2001, 2005) • Moscow Symposium on Logic, Algebra and Computation, February 8-10, 2006, Steklov Mathematical Institute, Moscow (Invited Lecture) • Symposium Contemporary Mathematics and its Applications. In honor of Prof. R. Gamkrelidze, Batumi, September 17-21, 2007 (Symposium Organizer) • International Conference Antalya Algebra Days, Antalya Cebir Günler: IX, Brian Hartley’ in Anisina, Antalya, May 21-25, 2007 (Invited Lecture) • International Conference Antalya Algebra Days, Antalya, May 21-25, 2007 (Invited Lecture) • European Mathematical Congress, Amsterdam, 2008 • International Algebraic Congress on the Occasion of 100-th anniversary of Prof. A. G. Kurosh, Moscow, May 2008 (Invited Lecture) | |
| Participation in Grant Projects | |
| Languages | |
| Georgian (native speaker), Russian (native speaker), English (fluent), Italian (well) | |
| Scientific interests | |
| Lie algebras and groups, geometric algebra, lattice theory | |
| Current scientific activities | |
| Future work plans | |
| . | |
| Department | |
| Theoretical Foundations in Mathematics |