Birational Equivalences and Generalized Weyl Algebra

Key Points

• Localized Hochschild homologies are computed for quantum groups and Podleś spheres, revealing interesting structures.
• Every generalized Weyl algebra is birationally equivalent to a smash product with a 1-torus, emphasizing underlying connections.
• The birational equivalence problem is addressed and solved, offering insights into smoothness conditions for generalized Weyl algebras.
• These findings can enhance understanding of various algebraic structures and their interrelations in mathematics.