HOMOLOGICAL INTEGRAL OF HOPF ALGEBRAS

By D. Lu, Q.-S. Wu, James J. Zhang. 2005

59 citations recorded by the source corpus.

The left and right homological integrals are introduced for a large class of infinite dimensional Hopf algebras. Using the homological integrals we prove a version of Maschke's theorem for infinite dimensional Hopf algebras. The generalization of Maschke's theorem and homological integrals are the keys to studying noetherian regular Hopf algebras of Gelfand-Kirillov dimension one.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/45c05cbe341e766aa618fa78452ad3155a1ea96f

How researchers see this paper

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

In Algebra and Number Theory

1. James J. Zhang
2. K. Goodearl
3. Kenneth A. Brown
4. D. Rogalski
5. Manuel Reyes
6. U. Krähmer
7. G. Abrams
8. Kulumani M. Rangaswamy

In Geometry and Topology

1. James J. Zhang
2. K. Goodearl
3. Kenneth A. Brown
4. D. Rogalski
5. Manuel Reyes
6. U. Krähmer
7. Amnon Yekutieli
8. Arkady Berenstein

In Mathematical Physics

1. Kenneth A. Brown
2. James J. Zhang
3. K. Goodearl
4. D. Rogalski
5. Manuel Reyes
6. G. Abrams
7. Amnon Yekutieli
8. Kulumani M. Rangaswamy

Citations in the corpus

• Noetherian Hopf algebra domains of Gelfand-Kirillov dimension two (2009, methodology): “For example, the homological integral was introduced for Artin-Schelter Gorenstein noetherian Hopf algebras [18], and it became a powerful tool in the classification of prime regular Hopf algebras of Gelfand-Kirillov dimension one [10].”
• Skew Calabi–Yau algebras and homological identities (2013, methodology): “tool in the theory of the finite-dimensional Hopf algebras His the notion of integrals [Mo, Chapter 2]. The theory of integrals has been extended to infinite-dimensional AS-Gorenstein Hopf algebras Hin [LuWZ2]. The left homological integral of such an H is defined to be the 1-dimensional H-bimodule Rl ”
• Prime regular Hopf algebras of GK‐dimension one (2008, methodology): “Classical components in GK-dimension one In preparation for the work on Hopf algebras of GK-dimension one which will occupy the rest of the paper, we state here as our starting point what can immediately be written down about such an algebra using the results in [12] and the concepts introduced in t”
• Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras (2006, methodology): “(a) By [ LWZ , Lemma 5.3(g)], io(A) is finite.”