Abstract. In this part one of a series of papers, we introduce a new version of quantum covering and super groups with no isotropic odd simple root, which is suitable for the study of integrable modules, integral forms and the bar involution. A quantum covering group involves parameters q and π with π 2 = 1, and it specializes at π = −1 to a quantum supergroup. Following Lusztig, we formulate and establish various structural results of the quantum covering groups, including a bilinear form, quasi-R-matrix, Casimir element, character formulas for integrable modules, and higher Serre relations.

We introduce a non-degenerate bilinear form and use it to provide a new characterization of quantum Kac-Moody superalgebras of anisotropic type. We show that the spin quiver Hecke algebras introduced by Kang, Kashiwara and Tsuchioka provide a categorification of half the quantum Kac-Moody superalgebras, using the recent work of Ellis-Khovanov-Lauda. A new idea here is that a supersign is categorified as spin (i.e., the parity-shift functor).

Abstract. Following Kashiwara's algebraic approach, we construct crystal bases and canonical bases for quantum supergroups of anisotropic type and for their integrable modules.

We construct the finite dimensional simple integral modules for the (degenerate) affine Hecke-Clifford algebra (AHCA),

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