# Plamen Koshlukov

Welcome! I am professor in Algebra at the Department of Mathematics, State University of Campinas.

My research interests lie in the area of Ring Theory: algebras with polynomial identities (2010 MSC 16Rxx), Lie and Jordan algebras (17Bxx and 17Cxx), Graded rings (16W22, 16W50, 16W55, 15A75)

IMECC, UNICAMP, R. Sergio Buarque de Holanda, 651
Cidade Universitaria Zeferino Vaz, Barao Geraldo, Campinas, SP, postcode (CEP) 13083-859, BRAZIL;
sala 347, IMECC, phone (++55) (19) 3521 6002, fax (++55) (19) 3289 5766

e-mail:   <my_first_name_in_lowercase>@ime.unicamp.br
An alternative e-mail address (but one I do not read very often) is the following:
<my_first_name_in_lowercase>.<my_last_name_in_lowercase>@gmail.com     (
see above for the correct spelling)

Sejam bem-vindos! Meus interesses científicos estão na área de álgebra: álgebras com identidades polinomiais (2010 MSC 16Rxx), álgebras de Lie e de Jordan (17Bxx e 17Cxx), Anéis graduados (16W22, 16W50, 16W55, 15A75).

Disciplinas do 1o semestre de 2020:

1. MA 141, Turma B: Geometria Analítica e Vetores. Aulas: Terça, 8-10 (sala CB 08), e Quinta, 8-10 (sala CB 08)

2. MM 455, Álgebras com Identidades Polinomiais. Aulas:  (sala IMECC ) e (sala IMECC ).

Disciplina do 2o semestre de 2020:
MM 439, Álgebras de Lie. Aulas: terça, 8-10 e quinta, 8-10, via Google Meet.
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CAPES - PRINT ALGEBRA - INFORMATION

### Mathematical Reviews, Matches for P. Koshlukov, (Requires access to the MathSciNet)

If you have no such an access, below is a (more or less) up-to-date list
(You might want to consult  the CNPq home page: http://www.cnpq.br, and then choose the Lattes Platform. There you may find fairly updated list of my publications as well as other relevant info. The site is free, no access fee is required. Here is the link to my CV there )

In case you need a copy of a paper let me know. For most of the papers below I can send you the pdf file. Most likely it won't be an exact copy of  the printed version but close enough. This way we are not running into problems with the copyright owners and similar issues... You can also find some of these (especially more recent ones)  at the ArXiv site.

1. Algebraic extensions and Baer and Jacobson radicals, Proc.13th Spring Conf., UBM, Sofia, 1984, 152--156.

2. On Lie T-ideals having small growth of the codimension sequence, with V. Drensky, Pliska 1986(8), 94--100.

3. Polynomial identities for a family of simple Jordan algebras, C.R.Acad. Bulg. Sci. 39, 1986, 15--17.

4. Polynomial identities for quadratic Jordan algebras, with V. Drensky, C.R.Acad. Bulg. Sci. 40, 1987, 5--8.

5. Weak polynomial identities for the vector space with a symmetric bilinear form, with V. Drensky, Proc. 16th Spring Conf., UBM, Sofia, 1987, 213--219.

6. Polynomial identities for a family of simple Jordan algebras, Commun. Algebra 16(7), 1988, 1325--1371.

7. Rational Hilbert series of relatively free Jordan algebras, J. Algebra 121(2), 1989, 301--309.

8. Polynomial identities for Jordan algebras of degree two, with V. Drensky, J. Indian Math. Soc. 55, 1990, 1--30.

9. Polynomial identities for Jordan pairs, Commun. Algebra 22(8), 1994, 2749--2769.

10. Special Jordan pairs, Commun. Algebra 23(9), 1995, 2457--2480.

11. Symmetric elements in free associative pairs over a field of characteristic two, Ann. Univ. Sofia , Fac. Math. Inf. , to appear (if ever???), 1996.

12. Speciality of Jordan pairs, An. Stiint. Univ."Ovidius" Constanta 4, 1996, f. 2, 86--94.

13. Weak polynomial identities for the matrix algebra of order two, J. Algebra 188, 1997, 610--625.

14. Some applications of invariant theory to P.I. algebras, Atas, V ENAL, USP, 1997, 85--96.

15. Finitely based ideals of weak polynomial identities, Commun. Algebra 26(10), 1998, 3335--3359.

16. Algebras with Polynomial Identities, Matem. Contemp. 16, 1999, 137--186.

17. Identities in Grassmann algebras in characteristic p>0 , with A. Giambruno, Atas, VIII ENAL, USP, 1999, 47--51.

18. Ideals of identities of representations of nilpotent Lie algebras, Commun. Algebra 28 (7), 2000, 3095--3113.

19. On the identities of the Grassmann algebras in characteristic p>0, with A. Giambruno, Israel J. Math. 122, 2001, 305--316.

20. Basis of the identities of the matrix algebra of order two over a field of characteristic p>2, J. Algebra 241, no. 1, 2001, 410--434.

21. Graded identities for T-prime algebras over fields of positive characteristic, with S. Azevedo, Israel J. Math. 122, 2002, 157--176.

22. A basis for the graded identities of the matrix algebra of order two over a finite field of characteristic $p\not= 2$, with S. Azevedo, Finite Fields Appl. 8, no. 4, 2002, 597--609.

23. Polynomial identities in T-prime algebras. IX Algebra Meeting USP/UNICAMP/UNESP (Portuguese) (São Pedro, 2001). Resenhas 5, no. 2, 2001, 91--105.

24. Central polynomials in the matrix algebra of order two, with J. Colombo, Atas, IX ENAL, USP, 2001, 89-92, Linear Algebra Appl. 377, 2004, 53--67.

25. Graded identities for the algebra of nxn upper triangular matrices over an infinite field, with A.Valenti, Intern. J. Algebra Comput. 13, no. 5, 2003, 517--526.

26. Graded and ordinary polynomial identities in matrix and related algebras, Lect. Notes Pure Appl. Math. 235, Marcel Dekker, 2003, 359--381.

27. Gradings on the algebra of upper triangular matrices and their graded identities, with O. M. Di Vincenzo, A.Valenti, J. Algebra 275, no.2, 2004, 550--566.

28. Tensor product theorems in positive characteristic, with S. Azevedo, M. Fidelis, J. Algebra  276, no. 2,  2004, 836--845.

29. Graded identities and PI equivalence of algebras in positive characteristic, with S. Azevedo, M. Fidelis, Commun. Algebra 33, no. 4, 2005, 1011--1022.

30. Identities with involution for the matrix algebra of order two in characteristic $p$, with J. Colombo, Israel J. Math. 146, 2005, 337--355.

31. Gradings and graded identities for the upper triangular matrices over an infinite field, with O. M. Di Vincenzo, A. Valenti, Groups, rings and group rings, 91--103, Lect. Notes Pure Appl. Math., 248, Chapman & Hall, Boca Raton, FL, 2006.

32. Polynomial identities of algebras in positive characteristic, with S. Mota Alves, J. Algebra 305 (2006), no. 2, 1149--1165.

33. Involutions for upper triangular matrix algebras, with O. M. Di Vincenzo, R. La Scala, Adv. in Appl. Math. 37 (2006), no. 4, 541--568.

34. Central polynomials for ${\Bbb Z}_2$-graded algebras and for algebras with involution, with A. Brand\~ao, J. Pure Appl. Algebra 208 (2007), no. 3, 877--886.

35. A-identities for the Grassmann algebra: the conjecture of Henke and Regev, with D. Gon\c{c}alves, Proc. Amer. Math. Soc. 136 (2008), no. 8, 2711--2717.

36. Graded polynomial identities for the Lie algebra $sl_2(K)$, Internat. J. Algebra Comput. 18 (2008), no. 5, 825--836.

37. Polynomial identities for graded tensor products of algebras, with J. Freitas, J. Algebra 321 (2009), no. 2, 667--681.

38. Graded central polynomials for T-prime algebras, with S. M. Alves, A. Brand\~ao, Commun. Algebra 37 (2009), no. 6, 2008--2020.

39. Graded central polynomials for the matirx algebra of order two, with A. Brand\~ao, A. Krasilnikov, Monatsh. Math. 157 (2009), no. 3, 247--256.

40. Graded identities for Lie algebras, with A. Krasilnikov, D. Silva, Contemp. Math. 499 (2009), 181--188, Amer. Math. Soc., Providence, RI.

41. Graded identities for tensor products of matrix (super)algebras over the Grassmann algebra, with O. M. Di Vincenzo, E. Santulo Jr., Linear Algebra Appl. 432, no. 2-3 (2010), 780--795.

42. The central polynomials for the finite-dimensional Grassmann algebras, with A. Krasilnikov, E. Silva, Algebra Discr. Math. 3 (2009), 69--76.

43. The central polynomials for the Grassmann algebra, with A. Brand\~ao, A. Krasilnikov, E. Silva, Israel J. Math. 179 (2010), 127--144.

44. Identities and isomorphisms of graded simple algebras, with M. Zaicev, Linear Algebra Appl. 432 (2010), 3141--3148.

45. On the *-polynomial identities of $M_{11}(E)$, with O. M. Di Vincenzo, J. Pure Appl. Algebra 215 (2011), 262--275.

46. 2-graded polynomial identities for the Jordan algebra of the symmetric matrices of order two, with D. D. Silva, J. Algebra 327 (2011), 236--250.

47. A-identities for upper-triangular matrices: a question of Henke and Regev, with D. Gon\c{c}alves, Israel J. Math. 186 (2011), 407--426.

48. Polynomial identities for the Jordan algebra of upper triangular matrices of order 2, with F. Martino, J. Pure Appl. Algebra 216, no. 11 (2012), 2524--2532.

49. Gradings and graded identities for the matrix algebra of order two in characteristic 2, with J. C. dos Reis, Serdica Math. J. 38, no. 1--3 (2012), 189--198.

50. A basis for the graded identities of the pair (M_2(K), gl_2(K)), with A. Krasilnikov, Serdica Math. J. 38, no. 1--3 (2012), 497--506.

51. The centre of generic algebras of small PI algebras, with T. C. Mello, J. Algebra 375 (2013), 109--120.

52. On the polynomial identities of the algebra M_{11}(E), with T. C. Mello, Linear Algebra Appl. 438, no. 11 (2013), 4469--4482.

53. GK dimension of the relatively free algerba for sl_2, with G. G. Machado, Monatsh. Math. 175, no. 4 (2014), 543--553.

54. G-identities for the Lie algebra sl_2(C), with A. D. M. Mortari, J. Pure Appl. Algebra 219, no. 6 (2015), 2381--2395.

55. Z-graded identities for the Lie algebra W_1, with J. A. O. Freitas and A. Krasilnikov, J. Algebra 427, no. 1 (2015), 226--251.

56. Graded algebras with polynomial growth of their codimensions, with D. La Mattina, J. Algebra 434 (2015), 115--137.

57. GK-dimension of 2 x 2 2×2 generic Lie matrices, with V. Drensky and G. Machado, Publ. Math. Debrecen 89 (2016), no. 1--2, 125--135.

58. Graded A-identities for the matrix algebra of order two, with A. Brand\~ao and D. Gon\c{c}alves, Internat. J. Algebra Comput. 26 (2016), no. 8, 1617--1631.

59. On Z_p-graded identities and cocharacters of the Grassmann algebra, with O. M. Di Vincenzo and V. R. T. da Silva, Comm. Algebra 45 (2017), no. 1, 343--356.

60. Elementary gradings on the Lie algebra UT^{(−)}_n, with F. Yukihide, J. Algebra 473 (2017), 66--79.

61. Group gradings on the Lie algebra of upper triangular matrices, with F. Yukihide, J. Algebra 477 (2017), 294--311.

62. Group gradings on the Lie and Jordan algebras of upper triangular matrices, with F. Yukihide and E. Hitomi, Sao Paulo J. Math.Sci. 11, no. 2 (2017), 326--347.

63. Asymptotics of graded codimension of upper triangular matrices, with F. Yukihide, Israel J. Math. 223, no. 1 (2018), 423--439.

64. Group gradings on the Jordan algebra of upper triangular matrices, with F. Yukihide, Linear Algebra Appl. 534 (2017), 1--12.

65. Embeddings for the Jordan algebra of a bilinear form, with C. Fidelis, D. Diniz, Adv. Math. 337 (2018), 294--316.

66. Z_2 and Z-graded central polynomials of the Grassmann algebra, with A. Guimar\~aes and C. Fidelis, Internat. J. Algebra Comput., to appear (2019).

67. Codimension growth for polynomial identities of representations of Lie algebras, with D. L. Mac\^edo, Math. Nachr., to appear (2020).

68. Codimension growth for weak polynomial identities, and non-integrality of the PI exponent, with D. L. Mac\^edo, Proc. Edinburgh Math. Soc., to appear (2020).

69. Trace identitties and almost polynomial growth, with A. Ioppolo and D. La Mattina, J. Pure Appl. Algebra, to appear (2020).