scholarly journals Matrix De Rham Complex and Quantum A-infinity algebras

2014 ◽  
Vol 104 (4) ◽  
pp. 373-395 ◽  
Author(s):  
S. Barannikov
Keyword(s):  
De Rham Complex ◽  
Rham Complex ◽  
De Rham

scholarly journals Integral calculus on quantum exterior algebras

2014 ◽  
Vol 11 (04) ◽  
pp. 1450026 ◽  
Author(s):  
Serkan Karaçuha ◽  
Christian Lomp
Keyword(s):  
Differential Calculus ◽  
Polynomial Algebra ◽  
Exterior Algebra ◽  
Integral Calculus ◽  
De Rham Complex ◽  
Integral Forms ◽  
Rham Complex ◽  
De Rham ◽  
Quantum Polynomial

Hom-connections and associated integral forms have been introduced and studied by Brzeziński as an adjoint version of the usual notion of a connection in non-commutative geometry. Given a flat hom-connection on a differential calculus (Ω, d) over an algebra A yields the integral complex which for various algebras has been shown to be isomorphic to the non-commutative de Rham complex (in the sense of Brzeziński et al. [Non-commutative integral forms and twisted multi-derivations, J. Noncommut. Geom.4 (2010) 281–312]). In this paper we shed further light on the question when the integral and the de Rham complex are isomorphic for an algebra A with a flat Hom-connection. We specialize our study to the case where an n-dimensional differential calculus can be constructed on a quantum exterior algebra over an A-bimodule. Criteria are given for free bimodules with diagonal or upper-triangular bimodule structure. Our results are illustrated for a differential calculus on a multivariate quantum polynomial algebra and for a differential calculus on Manin's quantum n-space.

scholarly journals Chiral de Rham Complex over Locally Complete Intersections

2015 ◽  
Vol 15 (2) ◽  
pp. 353-372
Author(s):  
Fyodor Malikov ◽  
Vadim Schechtman
Keyword(s):  
Complete Intersections ◽  
De Rham Complex ◽  
Rham Complex ◽  
De Rham

scholarly journals Duality symmetry of the p-form effective action and supertrace of the twisted de Rham complex

2003 ◽  
Vol 648 (3) ◽  
pp. 542-556 ◽  
Author(s):  
P. Gilkey ◽  
K. Kirsten ◽  
D. Vassilevich ◽  
A. Zelnikov
Keyword(s):  
Effective Action ◽  
De Rham Complex ◽  
Duality Symmetry ◽  
Rham Complex ◽  
De Rham

scholarly journals A discrete de Rham complex with enhanced smoothness

CALCOLO ◽  
2006 ◽  
Vol 43 (4) ◽  
pp. 287-306 ◽  
Author(s):  
Xue–Cheng Tai ◽  
Ragnar Winther
Keyword(s):  
De Rham Complex ◽  
Rham Complex ◽  
De Rham
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