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  • Db78tg00z?file=thumbnail
    Article
    Sethuraman, Bharath
    For each prime p and each n ≥ 1 (n ≥ 2 if p = 2), examples are constructed of a Galois extension K∕F whose Galois group has exponent pn and a central simple F-algebra A of exponent p which is split by K but is not in the Dec group of K∕F.
  • Work
    Article
    Kumar, K. Raj
    For the quasi-static, Rayleigh-fading multiple-input multiple-output (MIMO) channel with transmit and receive antennas, Zheng and Tse showed that there exists a fundamental tradeoff between diversity and spatial-multiplexing gains, referred to as the . . .
  • Work
    Article
    Sivic, Klemen
    We show that for all $ k\ge 1$ there exists an integer $ N(k)$ such that for all $ n\ge N(k)$ the $ k$-th order jet scheme over the commuting $ n\times n$ matrix pairs scheme is reducible. At the other end of the spectrum, it is known that for all $ k . . .
  • 1g05ff78h?file=thumbnail
    Article
    Jonov, Boyan
    We consider the affine variety Zm,n2,2 of first-order jets over Zm,n2, where Zm,n2 is the classical determinantal variety given by the vanishing of all 2×2 minors of a generic m×n matrix. When 2<m≤n, this jet scheme Zm,n2,2 has two irreducible compone . . .
  • Work
    Article
    Sethuraman, Bharath
    We present some general techniques for constructing full-rank, minimal-delay, rate at least one space-time block codes (STBCs) over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras (field extension . . .
  • Work
    Article
    Guralnick, Robert M.
    In this note, we show that the set of all commuting d-tuples of commuting n×n matrices that are contained in an n-dimensional commutative algebra is a closed set, and therefore, Gerstenhaber's theorem on commuting pairs of matrices is a consequence of . . .
  • Vx021j58w?file=thumbnail
    Article
    Sethuraman, Bharath
    Let F be a Henselian valued field with char(F) =/2, and let S be an inertially split F-central division algebra with involution sigma* that is trivial on an inertial lift in S of the field Z(S). We prove necessary and sufficient conditions for S to co . . .
  • Work
    Article
    Sethuraman, Bharath
    We study components and dimensions of higher-order determinantal varieties obtained by considering generic m×n (m⩽n) matrices over rings of the form F[t]/(tk), and for some fixed r, setting the coefficients of powers of t of all r×r minors to zero. Th . . .
  • Work
    Article
    Markin, Nadya
    We study fast lattice decodability of space-time block codes for n transmit and receive antennas, written very generally as a linear combination Σi=12l si Ai, where the si are real information symbols and the Ai are n×n ℝ-linearly independent complex- . . .