Related papers: Adams operations on classical compact Lie groups

In this paper, extending the results in \cite{F}, we compute Adams operations on twisted $K$-theory of connected, simply-connected and simple compact Lie groups $G$, in both equivariant and nonequivariant settings.

We show that the Adams operations in complex K-theory lift to operations in smooth K-theory. The main result is a Riemann-Roch type theorem about the compatibility of the Adams operations and the integration in smooth K-theory.

We construct ergodic actions of compact quantum groups on C^*-algebras and von Neumann algebras, and exhibit phenomena of such actions that are of a different nature from ergodic actions of compact Lie groups. In particular, we construct:…

A p-local compact group is an algebraic object modelled on the p-local homotopy theory of classifying spaces of compact Lie groups and p-compact groups. In the study of these objects unstable Adams operations, are of fundamental importance.…

The Adams operations $\psi_\Lambda^n$ and $\psi_S^n$ on the Green ring of a group $G$ over a field $K$ provide a framework for the study of the exterior powers and symmetric powers of $KG$-modules. When $G$ is finite and $K$ has prime…

In this paper we consider some Lie groups in complexified Clifford algebras. Using relations between operations of conjugation in Clifford algebras and matrix operations we prove isomorphisms between these groups and classical matrix groups…

We define quantum deformations of Adams operations in $K$-theory, in the framework of quasimap quantum $K$-theory. They provide $K$-theoretic analogs of the quantum Steenrod operations from equivariant symplectic Gromov--Witten theory. We…

We construct Adams operations on the rational higher arithmetic K-groups of a proper arithmetic variety. The definition applies to the higher arithmetic K-groups given by Takeda as well as to the groups suggested by Deligne and Soule, by…

We consider the Green ring $R_{KC}$ for a cyclic $p$-group $C$ over a field $K$ of prime characteristic $p$ and determine the Adams operations $\psi^n$ in the case where $n$ is not divisible by $p$. This gives information on the…

We analyze the structure of the virtual (orbifold) K-theory ring of the complex orbifold P(1,n) and its virtual Adams (or power) operations, by using the non-Abelian localization theorem of Edidin-Graham. In particular, we identify the…

Adams operations are the natural transformations of the representation ring functor on the category of finite groups, and they are one way to describe the usual lambda-ring structure on these rings. From the representation-theoretical point…

Let G be a finite group and K a number field. We show that the "k-th Adams operation" defined by Cassou-Nogues and Taylor on the locally free class group Cl(Z_K G) is a symmetric power operation, if k is coprime to the order of G. Using the…

We prove the classical Riemann-Roch theorems for the Adams operations $\,\psi^j\,$ on $K$-theory: a statement with coefficients on $\mathbb{Z}[j^{-1}]$, that holds for arbitrary projective morphisms, as well as another one with integral…

A $p$-local compact group is an algebraic object modelled on the homotopy theory associated with $p$-completed classifying spaces of compact Lie groups and p-compact groups. In particular $p$-local compact groups give a unified framework in…

Let $A$ be one of the following Clifford algebras : $\mathbb{R}_2 \cong \mathbb{H}$ or $\mathbb{R}_3$. For the algebra $A$, the automorphism group $Aut(A)$ and its invariants are well known. In this paper we will describe the invariants of…

Symplectic slice theorems elucidate the local structure of symplectic manifolds carrying Hamiltonian actions of compact Lie groups. We generalize these theorems in two natural settings. The first is based on the idea that complex reductive…

We consider a compact Lie group as a framed manifold equipped with the left invarianat framing $\mathscr{L}$. In a previous paper we have proved that the Adams $e_\mathbb{C}$-invariant value of $SU(2n)$ $(n\ge 2)$ gives a generator of the…

In this paper we will outline elements of the global calculus of seudo-differential operators on the group SU(2). This is a part of a more general approach to pseudo-differential operators on compact Lie groups that will appear in the…

Let $A=\underrightarrow{\lim}{A_n}$ be an AF algebra, $G$ be a compact group. We consider inductive limit actions of the form $\alpha=\underrightarrow{\lim}{\alpha_n}$, where $\alpha_n\colon G\curvearrowright A_n$ is an action on the finite…

This very rough sketch is a sequel to arXiv:1808.08587; it presents evidence that operations on lifts of the functors K(n) to cohomology theories with values in modules over valuation rings of local number fields, indexed by Lubin-Tate…