(A class of) Hodge duality operators over the quantum \(\mathrm{SU}(2)\) (Q423703)

The context of this paper is the study of the non-commutative geometry of the quantum \(\mathrm{SU}_q(2)\). The author introduces a notion of Hodge operators on the exterior algebra \(\Omega(\mathrm{SU}_q(2))\). The construction parallels the classical setting, where a metric \(g\) on a Lie group \(G\) of dimension \(N\), induces (fixing an orientation) a Hodge duality operator NEWLINE\[NEWLINE \Omega^k(G)\to \Omega^{N-k}(G). NEWLINE\]NEWLINE The Hodge operators introduced in \(\Omega(\mathrm{SU}_q(2))\) have diagonal squares, and their spectra show the same degeneracy of the antisymmetrizers of the first order bicovariant calculus in \(\mathrm{SU}_q(2)\).