How to navigate/focus to the next item in Angular2?

Create a focus directive (and register it in your NgModule) that calls focus() on the host element when the input value changes to true:

@Directive({
  selector : '[myFocus]'
})
class MyFocus {
  constructor(public renderer: Renderer, public elementRef: ElementRef) {}

  @Input()
  set myFocus(value :boolean) {
    if(value) {
      this.renderer.invokeElementMethod(
          this.elementRef.nativeElement, 'focus', []);
    }
  }
}

Add the selector and a binding that passes true or false to the directive when it is supposed to be focused:

<li *ngFor = "let work of works let idx=index" tabindex="-1" 
    [myFocus]="idx == focusedIdx" (keydown.ArrowDown)="handleKeyEvent( $event, 'Arrow Down' )">

Update focusedIdx on key events:

       handleKeyEvent(event: Event): void {
            this.focusedIdx++;
        }

See also Angular 2: Focus on newly added input element