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We construct via generators and relations, generalized Weil representations for analogues of classical SL(2, k), k a field, over involutive base rings (A, * ). This family of groups covers different kinds of groups, classical and non classical. We give some examples that include symplectic groups as well as non classical groups like SL * (2, Am), where Am is the finite modular analogue of the algebra of real m-jets in one dimension with its canonical involutive symmetry.2010 Mathematics Subject Classification. Primary 20C33; Secondary 20H25.

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