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| Author | : Andrew R. Kustin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 97 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821820737 |
This book is intended for graduate student and research mathematicians interested in commutative rings and algebras.
| Author | : Bruce Normansell Allison |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 175 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821828118 |
Introduction The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra, $r\ge 3$ (excluding type $\mathrm{D}_3)$ Models for $\mathrm{BC}_r$-graded Lie algebras, $r\ge 3$ (excluding type $\mathrm{D}_3)$ The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Central extensions, derivations and invariant forms Models of $\mathrm{BC}_r$-graded Lie algebras with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Appendix: Peirce decompositions in structurable algebras References.
| Author | : Yasuro Gon |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 130 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821827634 |
Obtains an explicit formula for generalized Whittaker functions and multiplicity one theorem for all discrete series representations of $SU(2,2)$.
| Author | : John Harold Palmieri |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 193 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 0821826689 |
This title applys the tools of stable homotopy theory to the study of modules over the mod $p$ Steenrod algebra $A DEGREES{*}$. More precisely, let $A$ be the dual of $A DEGREES{*}$; then we study the category $\mathsf{stable}(A)$ of unbounded cochain complexes of injective comodules over $A$, in which the morphisms are cochain homotopy classes of maps. This category is triangulated. Indeed, it is a stable homotopy category, so we can use Brown representability, Bousfield localization, Brown-Comenetz duality, and other homotopy-theoretic tools to study it. One focus of attention is the analogue of the stable homotopy groups of spheres, which in this setting is the cohomology of $A$, $\mathrm{Ext}_A DEGREES{**}(\mathbf{F}_p, \mathbf{F}_p)$. This title also has nilpotence theorems, periodicity theorems, a convergent chromatic tower, and a nu
| Author | : Peter Niemann |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 137 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821828886 |
Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including $AE_3$.
| Author | : Jürgen Ritter |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 105 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821829289 |
This paper concerns the relation between the Lifted Root Number Conjecture, as introduced in [GRW2], and a new equivariant form of Iwasawa theory. A main conjecture of equivariant Iwasawa theory is formulated, and its equivalence to the Lifted Root Number Conjecture is shown subject to the validity of a semi-local version of the Root Number Conjecture, which itself is proved in the case of a tame extension of real abelian fields.
| Author | : Mikhail Anatolʹevich Lifshit︠s︡ |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 103 |
| Release | : 2002 |
| Genre | : Computers |
| ISBN | : 082182791X |
This text considers a specific Volterra integral operator and investigates its degree of compactness in terms of properties of certain kernel functions. In particular, under certain optimal integrability conditions the entropy numbers $e_n(T_{\rho, \psi})$ satisfy $c_1\norm{\rho\psi}_r0$.
| Author | : Armand Borel |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 153 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821827928 |
This text describes the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in the extended Dynkin diagram of the simply connected cover, together with the co-root integers and the action of the fundamental group. In the case of three commuting elements, we compute Chern-Simons invariants associated to the corresponding flat bundles over the three-torus, and verify a conjecture of Witten which reveals a surprising symmetry involving the Chern-Simons invariants and the dimensions of the components of the moduli space.
| Author | : Palle E. T. Jørgensen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 74 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 0821826883 |
Let $N\in\mathbb{N}$, $N\geq2$, be given. Motivated by wavelet analysis, this title considers a class of normal representations of the $C DEGREES{\ast}$-algebra $\mathfrak{A}_{N}$ on two unitary generators $U$, $V$ subject to the relation $UVU DEGREES{-1}=V DEGREES{N}$. The representations are in one-to-one correspondence with solutions $h\in L DEGREES{1}\left(\mathbb{T}\right)$, $h\geq0$, to $R\left(h\right)=h$ where $R$ is a certain transfer operator (positivity-preserving) which was studied previously by D. Ruelle. The representations of $\mathfrak{A}_{N}$ may also be viewed as representations of a certain (discrete) $N$-adic $ax+b$ group which was considered recently
| Author | : Steve Hofmann |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 129 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 0821826840 |
This memoir considers the Dirichlet problem for parabolic operators in a half space with singular drift terms. Chapter I begins the study of a parabolic PDE modelled on the pullback of the heat equation in certain time varying domains considered by Lewis-Murray and Hofmann-Lewis. Chapter II obtains mutual absolute continuity of parabolic measure and Lebesgue measure on the boundary of this halfspace and also that the $L DEGREESq(R DEGREESn)$ Dirichlet problem for these PDEs has a solution when $q$ is large enough. Chapter III proves an analogue of a theorem of Fefferman, Kenig, and Pipher for certain parabolic PDEs with singular drift terms. Each of the chapters that comprise this memoir has its own numbering system and list
