Homological algebra
Derived invariance of the Tamarkin–Tsygan calculus of an algebra
Comptes Rendus. Mathématique, Volume 357 (2019) no. 3, pp. 236-240.

We prove that derived equivalent algebras have isomorphic differential calculi in the sense of Tamarkin–Tsygan.

On montre que deux algèbres équivalentes par dérivation ont des calculs différentiels (au sens de Tamarkin–Tsygan) isomorphes.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.01.007
Armenta, Marco Antonio 1, 2; Keller, Bernhard 3

1 CIMAT A. C. Guanajuato, Mexico
2 IMAG, Université de Montpellier, CNRS, Montpellier, France
3 Université Paris-Diderot – Paris 7, Sorbonne Université, UFR de mathématiques, CNRS, Institut de mathématiques de Jussieu–Paris Rive Gauche, IMJ–PRG, Bâtiment Sophie-Germain, 75205 Paris cedex 13, France
@article{CRMATH_2019__357_3_236_0,
     author = {Armenta, Marco Antonio and Keller, Bernhard},
     title = {Derived invariance of the {Tamarkin{\textendash}Tsygan} calculus of an algebra},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {236--240},
     publisher = {Elsevier},
     volume = {357},
     number = {3},
     year = {2019},
     doi = {10.1016/j.crma.2019.01.007},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2019.01.007/}
}
TY  - JOUR
AU  - Armenta, Marco Antonio
AU  - Keller, Bernhard
TI  - Derived invariance of the Tamarkin–Tsygan calculus of an algebra
JO  - Comptes Rendus. Mathématique
PY  - 2019
SP  - 236
EP  - 240
VL  - 357
IS  - 3
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2019.01.007/
DO  - 10.1016/j.crma.2019.01.007
LA  - en
ID  - CRMATH_2019__357_3_236_0
ER  - 
%0 Journal Article
%A Armenta, Marco Antonio
%A Keller, Bernhard
%T Derived invariance of the Tamarkin–Tsygan calculus of an algebra
%J Comptes Rendus. Mathématique
%D 2019
%P 236-240
%V 357
%N 3
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2019.01.007/
%R 10.1016/j.crma.2019.01.007
%G en
%F CRMATH_2019__357_3_236_0
Armenta, Marco Antonio; Keller, Bernhard. Derived invariance of the Tamarkin–Tsygan calculus of an algebra. Comptes Rendus. Mathématique, Volume 357 (2019) no. 3, pp. 236-240. doi : 10.1016/j.crma.2019.01.007. http://www.numdam.org/articles/10.1016/j.crma.2019.01.007/

[1] Armenta, M.; Keller, B. Derived invariance of the cap product in Hochschild theory, C. R. Acad. Sci. Paris, Ser. I, Volume 355 (2017) no. 12, pp. 1205-1207

[2] Gelfand, I.M.; Daletskiĭ, Yu.L.; Tsygan, B.L. On a variant of noncommutative differential geometry, Dokl. Akad. Nauk SSSR, Volume 308 (1989) no. 6, pp. 1293-1297

[3] Happel, D. Triangulated Categories in the Representation Theory of Finite-Dimensional Algebras, London Mathematical Society Lecture Note Series, vol. 119, Cambridge University Press, Cambridge, UK, 1988

[4] Happel, D. Hochschild cohomology of finite-dimensional algebras, Paris, 1987/1988 (Lecture Notes in Mathematics), Volume vol. 1404, Springer, Berlin (1989), pp. 108-126

[5] Kassel, C. Cyclic homology, comodules and mixed complexes, J. Algebra, Volume 107 (1987), pp. 195-216

[6] Keller, B. Invariance and localization for cyclic homology of dg algebras, J. Pure Appl. Algebra, Volume 123 (1998), pp. 223-273

[7] B. Keller, Derived invariance of higher structures on the Hochschild complex, preprint, 2003, available at the author's home page.

[8] Keller, B. Hochschild cohomology and derived Picard groups, J. Pure Appl. Algebra, Volume 190 (2004), pp. 177-196

[9] Rickard, J. Derived categories and stable equivalence, J. Pure Appl. Algebra, Volume 61 (1989) no. 3, pp. 303-317

[10] Rickard, J. Derived equivalences as derived functors, J. Lond. Math. Soc. (2), Volume 43 (1991) no. 1, pp. 37-48

[11] Tamarkin, D.; Tsygan, B. Noncommutative differential calculus, homotopy bv algebras and formality conjectures, Methods Funct. Anal. Topol., Volume 6 (2000) no. 2, pp. 85-100

[12] Zimmermann, A. Fine Hochschild invariants of derived categories for symmetric algebras, J. Algebra, Volume 308 (2007) no. 1, pp. 350-367

Cited by Sources: