Boris L Tsygan

  • 483 Citations
1983 …2020
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Research Output 1983 2018

  • 483 Citations
  • 32 Article
  • 4 Conference contribution
  • 3 Chapter
  • 1 Editorial
2018
1 Citation (Scopus)

A microlocal category associated to a symplectic manifold

Tsygan, B. L., Jan 1 2018, Algebraic and Analytic Microlocal Analysis - AAMA, Evanston, Illinois, USA, 2012 and 2013. Hitrik, M., Tamarkin, D., Tsygan, B. & Zelditch, S. (eds.). Springer New York LLC, p. 225-337 113 p. (Springer Proceedings in Mathematics and Statistics; vol. 269).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Symplectic Manifold
Enriched Category
Deformation Quantization
Module
Local System

Preface

Hitrik, M., Tamarkin, D. E., Tsygan, B. L. & Zelditch, S. M., Jan 1 2018, In : Springer Proceedings in Mathematics and Statistics. 269, p. v-Xiv

Research output: Contribution to journalEditorial

2017

On quasi-classical limits of DQ-algebroids

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B. L., Jan 1 2017, In : Compositio Mathematica. 153, 1, p. 41-67 27 p.

Research output: Contribution to journalArticle

Classical Limit
2015

Deligne groupoid revisited

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B. L., Jul 7 2015, In : Theory and Applications of Categories. 30, p. 1001-1016 16 p., 29.

Research output: Contribution to journalArticle

Simplicial Set
Graded Lie Algebras
Groupoid
Differential Forms
Nerve
4 Citations (Scopus)

Formality theorem for gerbes

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B. L., Mar 9 2015, In : Advances in Mathematics. 273, p. 215-241 27 p.

Research output: Contribution to journalArticle

Gerbes
Formality
Deformation Theory
Gerbe
Vector Control
2012

Noncommutative Calculus and Operads

Tsygan, B. L., 2012, Topics in Noncommutative Geometry. Cortinas, G. (ed.). AMS-CMI, p. 19-66 48 p. (Clay Mathematics Proceedings; vol. 16).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2011

Algebraic index theorem for symplectic deformations of gerbes

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B. L., 2011, Noncommutative Geometry and Global Analysis. Connes, A., Gorokhovsky, A., Lesch, M., Pflaum, M. & Rangipour, B. (eds.). American Mathematical Society, p. 23-39 17 p. (Contemporary Mathematics; vol. 546).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Deformations of algebroid stacks

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B. L., Mar 1 2011, In : Advances in Mathematics. 226, 4, p. 3018-3087 70 p.

Research output: Contribution to journalArticle

Graded Lie Algebras
Groupoid
Gerbe
Characteristic Classes
Deformation Theory
5 Citations (Scopus)

Noncommutative calculus and the gauss–manin connection

Dolgushev, V. A., Tamarkin, D. E. & Tsygan, B. L., Jan 1 2011, Progress in Mathematics. Springer Basel, p. 139-158 20 p. (Progress in Mathematics; vol. 287).

Research output: Chapter in Book/Report/Conference proceedingChapter

Operad
Differential Calculus
Calculus
7 Citations (Scopus)

Proof of swiss cheese version of deligne's conjecture

Dolgushev, V. A., Tamarkin, D. E. & Tsygan, B. L., Oct 21 2011, In : International Mathematics Research Notices. 2011, 20, p. 4666-4746 81 p.

Research output: Contribution to journalArticle

Operad
Deformation Quantization
Associative Algebra
Isomorphic
Physics
2009
8 Citations (Scopus)

Formality theorems for hochschild complexes and their applications

Dolgushev, V., Tamarkin, D. E. & Tsygan, B. L., Nov 1 2009, In : Letters in Mathematical Physics. 90, 1, p. 103-136 34 p.

Research output: Contribution to journalArticle

Formality
polynomials
algebra
theorems
Polynomial Algebra
1 Citation (Scopus)

Oscillatory modules

Tsygan, B. L., Jun 1 2009, In : Letters in Mathematical Physics. 88, 1-3, p. 343-369 27 p.

Research output: Contribution to journalArticle

modules
Sheaves
Module
Deformation Quantization
Symplectic Manifold
2 Citations (Scopus)

Riemann–roch for real varieties

Bressler, P., Kapranov, M., Tsygan, B. L. & Vasserot, E., Jan 1 2009, Progress in Mathematics. Springer Basel, p. 125-164 40 p. (Progress in Mathematics; vol. 269).

Research output: Chapter in Book/Report/Conference proceedingChapter

Gerbe
Compact Manifold
Fiber
Family
Class
2008
5 Citations (Scopus)

Chern character for twisted complexes

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B. L., Jan 1 2008, Progress in Mathematics. Springer Basel, p. 309-324 16 p. (Progress in Mathematics; vol. 265).

Research output: Chapter in Book/Report/Conference proceedingChapter

Chern Character
Cyclic Homology
K-theory
Algebra
2007
29 Citations (Scopus)

Deformation quantization of gerbes

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B. L., Sep 10 2007, In : Advances in Mathematics. 214, 1, p. 230-266 37 p.

Research output: Contribution to journalArticle

Gerbes
Deformation Quantization
Gerbe
Graded Lie Algebras
Classify

On the Gauss-Manin Connection in Cyclic Homology

Tsygan, B., 2007, In : Methods of Functional Analysis and Topology. 13, p. 83

Research output: Contribution to journalArticle

22 Citations (Scopus)

The Homotopy Gerstenhaber Algebra of Hochschild Cochains of a Regular Algebra is Formal

Dolgushev, V., Tamarkin, D. & Tsygan, B. L., 2007, In : Journal of Noncommutative Geometry. 1, p. 1

Research output: Contribution to journalArticle

2005

The ring of differential operators on forms in noncommutative calculus

Tamarkin, D. E. & Tsygan, B. L., 2005, Graphs and Patterns in Mathematics and Theoretical Physics. Lyubich, M. & Takhtajan, L. (eds.). American Mathematical Society, p. 105-138 34 p. (Proceedings of Symposia in Pure Mathematics; vol. 73).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2004

Remarks on Modules over Deformation Quantization Algebras

Nest, R. & Tsygan, B., 2004, In : Moscow Mathematical Journal. 4, p. 911

Research output: Contribution to journalArticle

2002
18 Citations (Scopus)

Riemann-Roch theorems via deformation quantization, I

Bressler, P., Nest, R. & Tsygan, B., Apr 15 2002, In : Advances in Mathematics. 167, 1, p. 1-25 25 p.

Research output: Contribution to journalArticle

Deformation Quantization
Euler Class
Chern Character
D-module
Cocycle
13 Citations (Scopus)

Riemann-Roch theorems via deformation quantization, II1

Bressler, P., Nest, R. & Tsygan, B., Apr 15 2002, In : Advances in Mathematics. 167, 1, p. 26-73 48 p.

Research output: Contribution to journalArticle

Deformation Quantization
Theorem
2001
22 Citations (Scopus)

Cyclic formality and index theorems

Tamarkin, D. & Tsygan, B., May 1 2001, In : Letters in Mathematical Physics. 56, 2, p. 85-97 13 p.

Research output: Contribution to journalArticle

Formality
Operad
Index Theorem
algebra
theorems
10 Citations (Scopus)

Local formula for the index of a fourier integral operator

Leichtnam, E., Nest, R. & Tsygan, B., Jan 1 2001, In : Journal of Differential Geometry. 59, 2, p. 269-300 32 p.

Research output: Contribution to journalArticle

Fourier Integral Operators
Lie Algebroids
Characteristic Classes
Index Theorem
Michael Francis Atiyah
1999

Operations on Hochschild and Cyclic Complexes

Daletski, Y. & Tsygan, B. L., 1999, In : Methods of Functional Analysis and Topology.

Research output: Contribution to journalArticle

1997
2 Citations (Scopus)

A Riemann-Roch Type Formula for the Microlocal Euler Class

Bressler, P., Nest, R. & Tsygan, B., Dec 1 1997, In : International Mathematics Research Notices. 20, p. 1032-1043 12 p.

Research output: Contribution to journalArticle

Euler Class
1996
17 Citations (Scopus)

Formal deformations of symplectic manifolds with boundary

Nest, R. & Tsygan, B., Dec 1 1996, In : Journal fur die Reine und Angewandte Mathematik. 481, p. 27-54 28 p.

Research output: Contribution to journalArticle

Manifolds with Boundary
Symplectic Manifold
10 Citations (Scopus)

Formal Versus Analytic Index Theorems

Nest, R. & Tsygan, B., Dec 1 1996, In : International Mathematics Research Notices. 11, p. 556-564 9 p.

Research output: Contribution to journalArticle

Index Theorem
1995
125 Citations (Scopus)

Algebraic Index Theorem

Nest, R. & Tsygan, B., 1995, In : Communications in Mathematical Physics. 172, p. 223

Research output: Contribution to journalArticle

74 Citations (Scopus)

Algebraic index theorem for families

Nest, R. & Tsygan, B., Jan 1 1995, In : Advances in Mathematics. 113, 2, p. 151-205 55 p.

Research output: Contribution to journalArticle

Index Theorem
Family
1993

Notes on Differential Forms on Quantum Groups

Tsygan, B. L., 1993, In : Selcta Math. Sov.. 12, p. 75

Research output: Contribution to journalArticle

1992

On the localization of topological invariants

Gelfand, I. M. & Tsygan, B. L., May 1 1992, In : Communications in Mathematical Physics. 146, 1, p. 73-90 18 p.

Research output: Contribution to journalArticle

Topological Invariants
Universal Space
differential geometry
Differential Geometry
Form
1991
32 Citations (Scopus)

Hochschild and cyclic homology of quantum groups

Feng, P. & Tsygan, B., Oct 1 1991, In : Communications in Mathematical Physics. 140, 3, p. 481-521 41 p.

Research output: Contribution to journalArticle

Cyclic Homology
Hochschild Homology
homology
Quantum Groups
Hopf Algebra
1990

On a Variant of Noncommutative Differential Geometry

Daletskii, Y. L., Gelfand, I. M. & Tsygan, B. L., 1990, In : Soviet Math. Dokl.. 40, p. 422

Research output: Contribution to journalArticle

1986
1 Citation (Scopus)

Homologies of some matrix Lie superalgebras

Tsygan, B. L., Apr 1 1986, In : Functional Analysis and its Applications. 20, 2, p. 164-165 2 p.

Research output: Contribution to journalArticle

Lie Superalgebra
Homology
1985
29 Citations (Scopus)

Additive K-theory and crystalline cohomology

Feigin, B. L. & Tsygan, B. L., Apr 1 1985, In : Functional Analysis and its Applications. 19, 2, p. 124-132 9 p.

Research output: Contribution to journalArticle

Crystalline Cohomology
K-theory
Crystalline materials
1 Citation (Scopus)

Hamiltonian operators and Hochschild homologies

Daletskii, Y. L. & Tsygan, B. L., Oct 1 1985, In : Functional Analysis and Its Applications. 19, 4, p. 319-321 3 p.

Research output: Contribution to journalArticle

Hochschild Homology
Hamiltonians
Mathematical operators
Operator
1983
19 Citations (Scopus)

Cohomologies of Lie algebras of generalized Jacobi matrices

Feigin, B. L. & Tsygan, B. L., 1983, In : Functional Analysis and its Applications. 17

Research output: Contribution to journalArticle

Solid state physics
Jacobi Matrix
Algebra
Cohomology
Lie Algebra
19 Citations (Scopus)

The homology of matrix Lie algebras over rings and the Hochschild homology

Tsygan, B. L., Apr 30 1983, In : Russian Mathematical Surveys. 38, 2, p. 198-199 2 p.

Research output: Contribution to journalArticle

Hochschild Homology
Matrix Algebra
Homology
Lie Algebra
Ring