wide
闊 centers on spaciousness and breadth: something wide, open, or expansive. The single given meaning "wide" captures the core idea of generous physical extent.
闊 combines 門 (gate) with 活, which likely contributes the sound and the idea of flowing or spreading, suggesting a gate that opens wide.
A gate 門 that is wide enough for lively activity 活 to flow through: 闊 means wide and spacious.
For カツ, imagine a wide gate that cuts across the landscape: cut -> カツ, and the gate is so wide it cuts through everything.
careless; thoughtless; stupid; heedless; unobservant; inadvertent; incautious
striding; swaggering; strutting
broad-minded; open-minded; openhearted; generous; magnanimous
not having met or contacted someone for a long time; neglect of friends
to apologize for a long neglect of friends (apologise)
generous; largehearted
spaciousness; extensiveness; expansiveness; vastness
upbeat and freehearted; cheerful and magnanimous
swaggering
magnanimous in one's attitude of mind; grand in one's idea or mind-set
free and easy; open and natural; not fastidious
very careless; quite thoughtless
broad-leaved tree
broad-minded and free in disposition; large-hearted and not scrupulous about trifles