Hodge decomposition for higher order Hochschild homology

By T. Pirashvili. 2000

168 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/437720e09ecdf2e5825408b93737ba9e22ca9e41

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Victor Turchin
2. G. Arone
3. Grégory Ginot
4. Steven V. Sam
5. Alan Robinson
6. Andrew Snowden
7. Bertrand Toën
8. Thomas Tradler

In Mathematical Physics

1. Victor Turchin
2. G. Arone
3. Grégory Ginot
4. Alan Robinson
5. Steven V. Sam
6. Bertrand Toën
7. Thomas Tradler
8. Andrew Snowden

Citations in the corpus

• Derived algebraic geometry (2014, background): “• The higher Hochschild cohomology HHn+1(X) is a global counter-part of the higher Hochschild cohomology of [98].”
• Hochschild and cyclic homology via functor homology (2002, methodology): “A description of Hochschild and cyclic homology of commutative algebras via homological algebra in functor categories was achieved in [4].”
• Graph-complexes computing the rational homotopy of high dimensional analogues of spaces of long knots (2011, methodology): “(2)The formality of C∗ ((Sm)•) is in fact the main reason for the Hodge splitting in the higher order Hochschild homology [29] for which our case is a particular example.”
• Hodge‐type decomposition in the homology of long knots (2010, background): “The E(2) term itself is isomorphic to the higher-order Hochschild homology [31] of the Γ-module Ad•: E(2) HH [k] ∗ (Ad•) HH [k] ∗ (Dd•).”
• Gröbner methods for representations of combinatorial categories (2014, background): “ In [Wi] analogs of FI for other classical Weyl groups are studied. In [WG] the category FA of finite sets with all maps is studied. The category Γ of pointed finite sets (and its opposite), appears in [Pi2] and [Ri1] in the contexts of Hochschild homology and Goodwillie calculus. • The category FSG o”
• Notes on factorization algebras, factorization homology and applications (2013, background): “s higher Hochschild homology and has been studied (in various guise) since at least the end of the 90s (see the approach of [EKMM, MCSV] to topological Hochschild homology, or, the work of Pirashvili [P] which is closely related to G-homology). Though its axiomatic description is an easy corollary o”
• Higher Hochschild Homology, Topological Chiral Homology and Factorization Algebras (2010, methodology): “This is essentially due to Pirashvili [30].”
• Gamma homology, Lie representations and E∞ multiplications (2003, methodology): “In this section we use the theory of [10] and [11] to prove that the homology of the Ξ-complex is stable homotopy.”
• Derived Algebraic Geometry (2014, background): “• The higher Hochschild cohomology HHn+1(X) is a global counter-part of the higher Hochschild cohomology of [98].”